ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXV, 1 (2006)
p. 63 - 74
Universal bounds for global solutions of a diffusion equation
with a mixed local-nonlocal reaction term
P. P. Rouchon
Abstract.
In this paper we prove the
existence of a universal, i.e. independent of the initial data, bound for
global positive solutions of a diffusion
equation with a mixed local-nonlocal reaction term. Such results are already
known in some cases of local or nonlocal reaction terms.
Keywords:
Nonlinear parabolic equations, local and nonlocal reaction term, boundedness of
global solutions, a priori estimates, universal bounds.
AMS Subject classification: 35B35, 35K55, 35K57.
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