# sw NLPDE Z~i[

## 2010Nx̃Z~i[̋L^

EFuy[WiSFVÍGj]

2010 N 4 30 ijj 15:30  17:30
sw w@w 3 251
u
F (Éwj
u
Local well-posedness for the Kawahara equation
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{ułSobolevH^sɂKawaharȁll. ̖Ɋւ, Chen-Li-Miao-Wu('09) ͒ʏFouriermps>-7/4ŎԋǏIK 𓱂. XFourierm^̉e萸ɔf̂ɏC邱Ƃɂ, ̌ʂg ł, [_sŎԋǏIKؐ𓱂Ƃɐ. {uł͂̏ؖ̌ƂȂ o^]s<-2ɂĔK ؂ł邱Ƃ̏ؖ𒆐Sɘb.

2010 N 5 14 ijj 15:30  17:30
sw w@w 3 251
u
F} q (ޗǏqwj
u
Analyticity and smoothing effect for the fifth order KdV type equation
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KdVKẅł5KdV̏lɂčl@ D KdVKw̑ԖڂɌʏKdVɂẮCK.Kato-Ogawa('00)ɂ ԉ͓IȎԋǏ̑݋yѕʂؖĂD COԖڂɌ5KdVɂĂ͎ԉ͓Iȉ̑݋y ʂ͏ؖĂȂD ̌̈́C̋̂K.Kato-Ogawa̘_؂Kpł łD ŉX͂̓̔ɂčl@ƂC ͏OȂ΂ȂȂC ɂĂ͒ʏKdV̔]ŗpꂽ ؖ@萸ɂ邱ƂK.Kato-Ogawa̎@Kp\ɂȂD ̓Iɂ́CFourierm(Bourgainm)@Ƌ[pfL2LE 藝ɗp邱ƂɂC 5KdV^Cv̎ԉ͓IȎԋǏ̑݋yѕʂ 邱ƂoD {uł͂̌ʂɂĘbD

2010 N 5 21 ijj 15:30  17:30
sw w@w 3 251
u
˖{ ^P (sww@wȁj
u
CX^gȂJSl
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ȉ͑smȂƂĂ܂D i˖{̃AuXgNg{蔲j Taubes͂QONȏOɁČIȎF RpNgSl̏ɂ́C񎩖ȃCX^g iƌĂ΂C̔^Δ̉j ɑ݂Dŋ߁Ĉ͎ƂؖF 񎩖ȃCX^gȂCRpNgSl݂̂D ̒藝ɂĘbD

2010 N 6 1 iΗjj 15:30  17:30
sw w@w 3 251
u
u
Stability properties of Ekman boundary layers
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In this talk we investigate stability properties of Ekman boundary layers, which are stationary solutions of the Navier-Stokes system with rotation in the half space. We prove that the Ekman layer is asymptotically stable provided the Reynolds number is small enough and discuss further its decay rates. Finally, we investigate a different clase of perturbations, namely stochastic perturbations of these layers.

2010 N 6 11 ijj 15:30  17:30
sw w@w 3 251
u
{ (sw͌j
u
[}l̏̒a֐ɂ
uv|
ufʏ̗LEȐ֐͒萔łvC Ƃ͍C[r̒藝ƂĒmĂD ̔􉽂ւ̃AiW[ƂāCÉC uȗ񕉂ł郊[}l̗̏LEȒa֐͒萔łv ƂD Ă̌C̈ʉƂāCR[fBO ~jRb́uȗ񕉂ł郊[}l̏́C Œ肳ꂽxa֐ȂԂ LłvƂD{uł́CɍlׂC uC[}l̏ɔ񎩖ȁixj a֐݂邩v ƂɂĂbD

2010 N 6 18 ijj 15:30  17:30
sw w@w 3 251
u
o v (kCwj
u
ϓw֐Ԃɂpf̗LE
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ʏLebesgueԂɑ΂C萔łw֐p ʉ鎖ɂāCϓwLebesgueԂ͒D ̍uł́CKȏɂ̕ϓw ѕϓwLebesgueԏ̍pf̗LEɊւ ʂЉD

2010 N 6 25 ijj 15:30  17:30
sw w@w 3 251
u
i (kwj
u
porous medium̉ɑ΂H\"older]Ƃ̉p
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Ô͍porous medium̎ɑ΂H\"olderl. Ô͍Ȃporous medium̎ɑ΂H\"olderA͗lXȌ mĂ. ɑ΂, Ô͍porous medium̎ H\"olderADiBenedetto-Friedmanɂď\Ă邪, ؖ͗^ĂȂ悤ł. {uł, ނ̗^\g , porous medium̎ɑ΂H\"older]. H\"older]̉pƂ, ՊEIމKeller-Segeln̉̎ ɂQߋl@, Qߎ̏]̎̑zIɗ^.
iڂej

2010 N 7 2 ijj 15:30  17:30
sw w@w 3 251
u
Joules Nahas (University of Californiaj
u
On the persistent properties of solutions to semi-linear Schrodinger equations
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We study persistent properties of solutions to semi-linear Schrodinger equations in weighted spaces.

2010 N 7 9 ijj 15:30  17:30
sw w@w 3 251
u
aco G (pwj
u
The existence of positive solutions to the semilinear elliptic equation involving the Sobolev-Hardy critical terms
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{uł́CSobolev-Hardy ^ՊE𔺂ȉ~^̉𐫂ɂĘ_D ߔNCGhoussoub-Robert ɂ茴_LË̋EɈʒuC ̓_ł̕ϋȗƂ̉C Hardy-Sobolev ^ՊE𔺂ȉ~^̐l݂̑ؖꂽD ނ̌ʂ𓥂܂CXSobolev-Hardy^ՊEɉC ٓ_̒ʏSobolev ^ՊE𔺂ȉ~^̉𐫂l@C ނƓl̏̉C̐l̍\ɐD ؖɍۂCSobolev ^ՊE܂ޑȉ~^̐l\ Brezis-Nirenberg̎@ƂC ՊEP[X瓾ɑ΂锚͂sD

2010 N 7 13 iΗjjC14ijj
sw w@w 3 251
u
Benjamin Dodson (University of Californiaj
u
Global well-posedness and scattering for the defocusing, $L2$-critical, nonlinear Schrodinger equation when $d \geq 3$
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In these talks we will investigate the $L2$ critical Schrodinger initial value problem $i u_t+\Delta u=|u|^{4/d}u, \, u(0,x)=u_0$ in dimensions $d \geq 3$. We prove this using the concentration compactness method. We use an interaction Morawetz estimate localized to low frequencies.
uv|@um[g

2010 N 7 23 ijj 15:30  17:30
sw w@w 3 251
u
V T (wj
u
On the degenerate spectral gaps of the one-dimensional Schr\"odinger operators with the periodic $\delta^{(1)}$-interactions
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In this talk, we focus on the one-dimensional Schr\"odinger oprators with the periodic $\delta^{(1)}$-interactions, which are defined through the distribution theory for the discontinuous test functions. According to the Floquet-Bloch theory, its spectrum consists of the infinitely many closed intervals, which are called the bands of the spectrum. Consecutive bands are separated by an open set called the spectral gap. The main purpose of this talk is to determine whether the $j$-th spectral gap is degenerate or not for a given natural number $j$ by using the rotation number.

2010 N 9 3 ijj 15:30  17:30
sw w@w 3 251
u
u
Normal forms and the "upside-down" I method : growth of higher Sobolev norms for periodic NLS
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Bourgain used normal form reduction and the I-method to prove global well-posedness of one-dimensional periodic quintic NLS in low regularity. In this talk, we discuss the basic notion of normal form reduction for Hamiltonian PDEs and apply it to one-dimensional periodic NLS with general power nonlinearity. Then, we combine it with the "upside-down" I-method to obtain upperbounds on growth of higher Sobolev norms of solutions. In the case of cubic NLS, we explicitly compute the terms arising in the first few iterations of normal form reduction to improve the result. This is a joint work with James Colliander (University of Toronto) and Soonsik Kwon (KAIST).
uXCh

2010 N 10 1 ijj 15:30  17:30
sw w@w 3 251
u
O ב (_ˑwj
u
XP[ϊsϐƕsړsϐAQɂ
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XP[Eϊƕsړ͂ꂼꐳ̎Ȃ@Qyю ŜȂ@Q̋AȍpƌȂD Ŗ{uł́A̍pɑ΂ĕsςȋAQ̐ɂčl@D ܂Â悤ȒۓIgg ݂ɂA̎Ԗł̋ƎȑɊւǍ iBw̉BǍsƂ̋jɂďЉD

2010 N 10 8 ijj 15:30  17:30
sw w@w 3 251
u
(sww@wȁj
u
 Klein-Gordon ̊GlM[𒴂擮͊w
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Klein-Gordon ԂRC W񐫂̂RpōlD ͔̕U^̓T^łCUEǗgESĎD ܂CԁiljGlM[̒ႢŜ́C Ǝԑ摶݂̂Q̎ԕsςȊJW 鎖͗ǂmĂD ̍uł͊Ԃ菭GlM[܂ł̉Ŝ拓XɕނC ꂪ]P̒S葽l̂ƒSs葽l̂ɂ鉡fIȕɂė^鎖D ̂XƂ́CUEǗgÊR̑gݍ킹̐ꂼőSĎ蓾鎖ɑΉD Wilhelm Schlag (University of Chicago) Ƃ̋łD

2010 N 10 12 iΗjj 15:30  17:30
sw w@w 3 251
u
OY pV (wj
u
񈳏kNavier-Stokesɑ΂Liouville^藝Ƃ̉p
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uSԂɂLEȒa֐͒萔łvƂ 咣Liouville̒藝ƂĒmĂD ̕Δ̉ɑ΂Ăގ̎咣藧ƂmĂC ̋̌ɉpĂD{uł́C 3SԂɂ񈳏kNavier-StokešE扁EÑ)C ߋɖԑ݂ɑ΂Liouville^藝ЉD ܂CpĔ̉QxɊւConstantin-Fefferman̒藝l@ D(Vꎁ(w)Ƃ̋)

2010 N 10 15 ijj 13:00  15:00
sw w@w 3 251
u
u
Hamiltonian Systems and Invariant Measures
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This is an introductory lecture of Hamiltonian Systems and Invariant Measures.
um[g

2010 N 10 15 ijj 15:30  17:30
sw w@w 3 251
u
|c u (kwj
u
U^̉̑拓ɂ
uv|
U^̏lɂ, ԑ̑ݐyёQߋɂčl. uK(Hooke ̍)̗Lɂ{̌̕ωv y, uU^̊{ƏU^g̊{Ƃ̐̈Ⴂv ̐\𖾂炩ɂ, ̐]ɂ̉͂qׂ.

2010 N 10 22 ijj 13:00  15:00
sw w@w 3 251
u
u
Hamiltonian Systems and Invariant Measures 2
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This is a continuation of Part 1. First, I will discuss the integrability of the exponential weight with respect to the Wiener measure. Then, I will talk about the invariance of the Gibbs measure, when (1) there is an a priori GWP and (2) there is no a priori GWP.
um[g

2010 N 10 22 ijj 15:30  17:30
sw w@w 3 251
u
n B (sYƑwj
u
Asymptotic behavior of ground states of quasilinear Schrodinger equations
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In this talk, we consider quasilinear Schrodinger equations which appear in plasma physics. We study asymptotic behavior of ground states. This is a joint work with Shinji Adachi (Shizuoka University).

2010 N 11 12 ijj 15:30  17:30
sw w@w 3 251
u
{H qs (sw͌j
u
Bifurcation analysis to the Lugiato-Lefever equation in one space dimension
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We study the stability and bifurcation of steady states for a certain kind of damped driven nonlinear Schrodinger equation with cubic nonlinearity and a detuning term in one space dimension, mathematically in a rigorous sense. It is known by numerical simulations that the system shows lots of coexisting spatially localized structures as a result of subcritical bifurcation. Since the equation does not have a variational structure, unlike the conservative case, we cannot apply a variational method for capturing the ground state. Hence, we analyze the equation from a viewpoint of bifurcation theory. In the case of a finite interval, we prove the fold bifurcation of nontrivial stationary solutions around the codimension two bifurcation point of the trivial equilibrium by exact computation of a fifth-order expansion on a center manifold reduction. In addition, we analyze the steady-state mode interaction and prove the bifurcation of mixed-mode solutions, which will be a germ of localized structures on a finite interval. Finally, we study the corresponding problem on the entire real line by use of spatial dynamics. We obtain a small dissipative soliton bifurcated adequately from the trivial equilibrium. (This is a joint work with Prof. Isamu Ohnishi(Hiroshima University) and Prof. Yoshio Tsutsumi (Kyoto University).)

2010 N 11 16 iΗjj 15:30  17:30
sw w@w 3 552
u
a Iq (w|wj
u
Transversality of stable and Nehari manifolds for a semilinear heat equation
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It is well known that for the subcritical semilinear heat equation, negative initial energy is a sufficient condition for finite time blowup of the solution. We show that this is no longer true when the energy functional is replaced with the Nehari functional, thus answering negatively a question left open by Gazzola and Weth (2005). Our proof proceeds by showing that the local stable manifold of any non-zero steady state solution intersects the Nehari manifold transversally. As a consequence, there exist solutions converging to any given steady state, with initial Nehari energy either negative or positive. (This is a joint work with F. Dickstein, Ph. Souplet and F. Weissler.)

2010 N 11 19 ijj 14:00  15:00
sw w@w 3 251
u
Yong Zhou (Zhejiang Normal Universityj
u
On the Camassa-Holm equation
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I will give a detailed description on the corresponding solution for the Camassa-Holm equation with compactly supported initial datum. The description implies infinite propagation speed for the Camassa-Holm equation. We will also introduce a new and direct proof for McKean's theorem on wave breaking of the Camassa-Holm equation. Finally, some open problems will be listed.

2010 N 11 19 ijj 15:30  17:30
sw w@w 3 251
u
(wK@wj
u
̎wHartreẻ
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̎wHartreel. ͒᎟Schrodinger-Poissonn̈ʉƂČ, ő傷^. ̓GlM[NXɂ ̑摶݂̌ʂЉ. ^^|eV ̌ʂ܂ł, ̉e܂oƂƂȂ. , ȎwɂĂ͉zɋLqł,@ ʂɗ^^|eV̌ʂ^ʂɂ Iɑł邱ƂȂǂmFł.

2010 N 11 26 ijj 15:00  16:00
sw w@w 3 251
u
Yong Zhou (Zhejiang Normal Universityj
u
Some qualitative studies on the 3D incompressible Navier-Stokes equations
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In this talk, I will introduce some recent results on the 3D incompressile Navier-Stokes equations. Besides some regularity criteria for the Leray-Hopf weak solutions, I will list some results on asymptotic stability and introduce a new method to establish decay rate for weak solutions.

2010 N 11 26 ijj 16:30  18:30
sw w@w 3 251
u
Gv (kCwj
u
Well-posedness of the derivative nonlinear Sch\"{o}dinger equation on the one dimensional torus below $H^{1/2}$
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The $H^{1/2-}$ well-posedness is of some interest in several fields, as an example, in construction of the Gibbs measure (or Gaussian data) and Sobolev's embedding theorem. However $s=1/2$ of $H^{s}$ was the borderline regularity for which the well-posedness result holds true. In particular, the wide applicability of the standard criterion of the Fourier restriction norm method breaks down in $H^{1/2-}$. I shall discuss the local well-posedness in $H^{1/2-}$.

2010 N 12 17 ijj 15:30  17:30
sw w@w 3 251
u
Claudio Cacciapuoti (Hausdorff Center for Mathematicsj
u
Nonlinear Schroedinger Equation on Star Graphs: Scattering of Fast Solitons
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We define the Schroedinger equation with focusing, cubic nonlinearity on a star graph. We study the dynamics of a solitary wave in the high velocity regime. We show that after colliding with the vertex a soliton splits in reflected and transmitted components. Over a time scale of logarithmic order in the velocity, the mass spreads over the edges of the graph according to the reflection and transmission coefficients associated to the linear problem. Over the same time scale, the outgoing waves preserve a soliton character. In the analysis we follow ideas borrowed from the seminal paper about scattering of fast solitons by a delta interaction on the line, by Holmer, Marzuola and Zworski; our work represents an extension of their results to the case of graphs and, as a byproduct, it shows how to extend their analysis to the scattering of solitons by more singular point interactions on the line.

2011 N 1 7 ijj 15:30  17:30
sw w@w 3 251
u
Saburoh Saitoh (Aveiro Universityj
u
̉̍\ɂĐj̗_pVU@ɂ
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Δt̉vZ@ʏɕ\邽߂ɂ́C ͓IȉLvf@⍷@̂悤ɗUKvDŁC {Iȕ@ƂčĐj̗_pV^̗U@ЉD T͓͂o͂L̃f[^ƂāC 𖞂CӖł̍œKȉ\@łD ͗L̎ԂƋԂŕ𖞂œKȉ̍\@^D XɁCŋ߁C͂ɗL̃f[^w肵ƂɁC lĂVXe炠ӖŎRɌ܂C ͂̑Ŝ߂Ԗ@𓾂̂ŁCʘ_ƂƂɁC Mg̏ꍇɋ̓IȌʂЉD @ƂĂ̓Rmt̐@ƍĐj̗_pD e͐VCʓICflCwxłD

2011 N 1 11 iΗjj 14:00  15:00
sw w@w 3 552
u
Hendra Gunawan (Institute Technology of Bandungj
u
Stummel Class and Generalized Morrey Spaces (Part 1)
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A relation between the Stummel class and homogeneous Morrey spaces has been studied by Ragusa and Zamboni (2001). In this talk, we shall present an extension of their result on generalized Morrey spaces of homogeneous and non-homogeneous type.

2011 N 1 11 iΗjj 15:00  16:00
sw w@w 3 552
u
Idha Sihwaningrum (Jenderal Soedirman Universityj
u
Stummel Class and Generalized Morrey Spaces (Part 2)
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This is a continuation of the talk Part 1.

2011 N 1 14 ijj 15:30  17:30
sw w@w 3 251
u
c m (wj
u
Weighted norm inequalities for multilinear fractional operators on Morrey spaces
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The purpose of this talk is to introduce a weighted theory for multilinear fractional integral operators and multi(sub)linear fractional maximal operators in the framework of Morrey spaces. We give natural sufficient conditions for the one and two weight inequalities of these operators and, as a corollary, obtain the (so-called) Olsen inequality for multilinear fractional integral operators. The results are extensions to Morrey spaces of those due to Kabe Moen.

2011 N 1 21 ijj 15:30  17:30
sw w@w 3 251
u
~c TW (wj
u
On quenching and dead core at space infinity for semilinear heat equation with absorption
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We study quenching and dead core at space infinity for a semilinear heat equation with an absorption $u_t = \Delta u- u^{-p}$ with $p>-1$ and bounded initial data $u(x,0) = u_0 (x)$ satisfying $\inf_{x\in {\bf R}^d } =m>0$.
iڂej

2011 N 1 28 ijj 14:30  15:30
sw w@w 3 251
u
Yue Lie
u
Wave breaking phenomena and solitary waves for a generalized two-component Camassa-Holm system
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In this talk I propose and analyze a generalized two-component Camassa-Holm system which can be derived from the theory of shallow water waves moving over a linear shear flow. This new system also generalizes a class of dispersive waves in cylindrical compressible hyperelastic rods. I will show in the first part of the talk that this new system can still exhibit the wave-breaking phenomenon. I also establish a sufficient condition for global solutions. In the second part of the talk, I will study the solitary wave solutions of the generalized two-component Camassa-Holm system. In addition to those smooth solitary-wave solutions, I will show that there are solitary waves with singularities: peaked and cusped solitary waves. I also demonstrate that all smooth solitary waves are orbitally stable in the energy space.

2011 N 1 28 ijj 16:00  18:00
sw w@w 3 251
u
O ikwj
u
Imperfect bifurcation for the Liouville-Gel'fand equation on a perturbed annulus
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Dirichlet Eɂ Liouville-Gel'fand l@. ̈悪~̈̏ꍇ, ͕̕}LEɐLт鐳lΏ̉̎}, ɁC̎}ɂ͑Ώ̐󕪊_݂. {uɂĂ, ~̈ۓƂ̕}̕ωɂčl. ɑΏ̐󕪊_ɂ sS (_߂̉̎}؂, _) N邩ǂɂčl@.

2011 N 2 4 ijj 15:00  16:00
(͊wnZ~i[Ƃ̍J)
sw w@w 3 251
u
Clement Gallo iUniversite Montpellier 2j
u
Finite time extinction by nonlinear damping for the Schrodinger equation
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We consider the Schrodinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum.

2011 N 2 4 ijj 16:30  17:30
(͊wnZ~i[Ƃ̍J)
sw w@w 3 251
u
Nitsan Ben-Gal iThe Weizmann Institute of Science, Israelj
u
Attraction at Infinity: Constructing Non-Compact Global Attractors in the Slowly Non-Dissipative Realm
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One of the primary tools for understanding the much-studied realm of reactiondiffusion equations is the global attractor, which provides us with a qualitative understanding of the governing behaviors of solutions to the equation in question. Nevertheless, the classic global attractor for such systems is defined to be compact, and thus attractor theory has previously excluded such analysis from being applied to nondissipative reaction-diffusion equations.

In this talk I will present recent results in which I developed a non-compact analogue to the classical global attractor, and will discuss the methods derived in order to obtain a full decomposition of the non-compact global attractor for a slowly non-dissipative reaction-diffusion equation. In particular, attention will be paid to the nodal property techniques and reduction methods which form a critical underpinning of asymptotics research in both dissipative and non-dissipative evolutionary equations. I will discuss the concepts of the completed inertial manifold and non-compact global attractor? and show how these in particular allow us to produce equivalent results for a class of slowly non-dissipative equations as have been achieved for dissipative equations. Additionally, I will address the behavior of solutions to slowly non-dissipative equations approaching and at infinity, the realm which presents both the challenges and rewards of removing the necessity of dissipativity.

2011 N 2 8 iΗjj 14:00 ` 16:00
sw w@w 3 552
u
Tino Ullrich iBonn Universityj
u
Generalized coorbit space theory and atomic decompositions of Besov-Lizorkin-Triebel type functions spaces
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Coorbit space theory is an abstract approach to function spaces and their atomic decompositions. The original theory developed by Feichtinger and Grochenig in the late 1980ies heavily uses integrable representations of locally compact groups. Their theory covers, in particular, homogeneous Besov-Lizorkin-Triebel spaces, modulation spaces, Bergman spaces and the recent shearlet spaces. However, inhomogeneous Besov-Lizorkin-Triebel spaces cannot be covered by their group theoretical approach. Later it was recognized by Fornasier and Rauhut 2005 that one may replace coherent states related to the group representation by more general abstract continuous frames. In the rst part of the talk we show how to extend this abstract generalized coorbit space theory signi cantly in order to treat a wider variety of coorbit spaces. A uni ed approach towards atomic decompositions and Banach frames with new results for general coorbit spaces is presented. In the second part we apply the abstract setting to a speci c framework and study coorbits of what we call Peetre spaces. They allow to recover inhomogeneous Besov-Lizorkin-Triebel spaces of various types of interest as coorbits. We obtain several old and new wavelet characterizations based on explicit smoothness, decay, and vanishing moment assumptions of the respective wavelet. As main examples we obtain results for weighted spaces (Muckenhoupt, doubling), general 2-microlocal spaces, Besov-Lizorkin-Triebel-Morrey spaces, spaces of dominating mixed smoothness, and even mixtures of the mentioned ones. Due to the generality of our approach, there are many more examples of interest where the abstract coorbit space theory is applicable.