Quasi-linear Singular Parabolic Problem
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Date
2018
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Mathematics and Computer Science Department of Mathematics
Abstract
We investigate the following quasi-linear and singular parabolic equation ,
8><
>:
ut Δpu =
1
u + f(x; u) in QT ;
u = 0; on T ; u > 0 in QT ; (Pt)
u(0; x) = u0(x) in Ω:
WhereΩis an open bounded domain with smooth boundary inRN(withN 2), 1 < p < 1,
0 < , T > 0, QT = (0; T) Ω and T = (0; T) @Ω. We assume that f is bounded below
Caratheodory function and u0 2 W1;p
0 (Ω). In this memory we will study the existence and
uniqueness of the weak solution of (Pt) using method of semi- discretization in time and we
study the stabilization.
Description
Keywords
Quasi-linear and singular parabolic equation, existence and uniqueness of the weak solution, p-Laplacian, method of semi- discretization in time, sub- and super-solution .