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International Journal of Mathematics and Mathematical Sciences
Volume 1, Issue 1, Pages 21-29
http://dx.doi.org/10.1155/S0161171278000034

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

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

Received 17 February 1977; Revised 1 November 1977

Copyright © 1978 Hindawi Publishing Corporation. 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.

Abstract

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.