Electron. J. Diff. Equ., Vol. 2010(2010), No. 25, pp. 1-14.

Parabolic equations with Robin type boundary conditions in a non-rectangular domain

Arezki Kheloufi, Boubaker-Khaled Sadallah

In this article, we study the parabolic equation $\partial_{t}u-c^2(t)\partial_x^2u=f$ in the non-necessarily rectangular domain
 \Omega =\{ (t,x)\in\mathbb{R}^2:0<t<T,\,
The boundary conditions are of Robin type, while the right-hand side lies in the Lebesgue space $L^2(\Omega )$. Our aim is to find conditions on $c$ and the functions $(\varphi_i)_{i=1,2}$ such that the solution belongs to the anisotropic Sobolev space $H^{1,2}(\Omega )=\{u\in L^2(\Omega ):\partial_{t}u,
\partial_xu,\partial_x^2u\in L^2(\Omega )\} $. For goal we use the method of approximation of domains.

Submitted July 29, 2009. Published February 10, 2010.
Math Subject Classifications: 35K05, 35K20.
Key Words: Parabolic equation; non-rectangular domains; Robin condition; anisotropic Sobolev space.

Show me the PDF file (264 KB), TEX file, and other files for this article.

Arezki Kheloufi
Department of Sciences and Techniques, Faculty of Technology
Béjaia University, 6000. Béjaia, Algeria
email: arezkinet2000@yahoo.fr
Boubaker-Khaled Sadallah
Department of Mathematics, E.N.S.
16050 Kouba. Algiers, Algeria
email: sadallah@ens-kouba.dz

Return to the EJDE web page