International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 1, Pages 21-29

Explicit L2 inequalities for parabolic and pseudoparabolic equations with Neumann boundary conditions

J. R. Kuttler and V. G. Sigillito

Applled Physics Laboratory, The Johns Hopkins University, Laurel 20810, Maryland, USA

Received 17 February 1977; Revised 1 November 1977

Copyright © 1978 J. R. Kuttler and V. G. Sigillito. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Explicit L2 inequalities are derived for second and third order diffusion equations with Neumann boundary conditions. Such inequalities are useful in approximating solutions to partial differential equations by the method of a priori inequalities.