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Research Article Open Access

An Integral Two Space-Variables Condition for Parabolic Equations

A. L. Marhoune1 and F. Lakhal2
  • 1 University Mentouri Constantine, Algeria
  • 2 University 08 Mai 45, Algeria

Abstract

In this study, an integral two space-variables condition for a class of parabolic equations. The existence and uniqueness of the solution in the functional weighted Sobolev space were proved. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.

Journal of Mathematics and Statistics
Volume 8 No. 2, 2012, 185-190

DOI: https://doi.org/10.3844/jmssp.2012.185.190

Submitted On: 7 February 2012 Published On: 12 March 2012

How to Cite: Marhoune, A. L. & Lakhal, F. (2012). An Integral Two Space-Variables Condition for Parabolic Equations. Journal of Mathematics and Statistics, 8(2), 185-190. https://doi.org/10.3844/jmssp.2012.185.190

Open AccessCopyright: © 2012 A. L. Marhoune and F. Lakhal. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Integral boundary two space-variables condition
  • energy inequalities
  • weighted sobolev spaces