Year: 2019
Author: Qitong Ou, Huashui Zhan
Journal of Partial Differential Equations, Vol. 32 (2019), Iss. 3 : pp. 281–292
Abstract
In this article, we study the system with boundary degeneracy
$u_{it}-{\rm div}(a(x)|\triangledown u_{i}|^{p_{i}-2}\nabla u_i)=f_{i}(x,t,u_1,u_2),\qquad (x,t)\in\Omega_T$.
Applying the monotone iterattion technique and the regularization method, we get the existence of solution for a regularized system. Moreover, under an integral condition on the coefficient function $a(x)$, % And if %$ \int_{\Omega} a(x)^{-\frac{1}{min{(p_1,p_2)}-1}} {\rm d}x{\rm d}t\leq C ,$ the existence and the uniqueness of the local solutions of the system is obtained by using a standard limiting process. Finally, the stability of the solutions is proved without any boundary value condition, provided $a(x)$ satisfies another restriction.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v32.n3.5
Journal of Partial Differential Equations, Vol. 32 (2019), Iss. 3 : pp. 281–292
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Weak solution