Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 116, pp. 1-14.

Title: Resolutions of parabolic equations in non-symmetric conical domains
  
Author: Arezki Kheloufi (Bejaia Univ., Bejaia, Algeria)

Abstract:
 This article is devoted to the analysis of a two-space dimensional
 linear parabolic equation, subject to Cauchy-Dirichlet boundary
 conditions. The problem is set in a conical type domain and the
 right hand side term of the equation is taken in a Lebesgue space.
 One of the main issues of this work is that the domain can possibly
 be non regular. This work is an extension of the symmetric case
 studied in Sadallah [13].

Submitted May 31, 2012. Published July 09, 2012.
Math Subject Classifications: 35K05, 35K20.
Key Words: Parabolic equation; conical domain; anisotropic Sobolev space.