Parabolic System Related to the P-Laplician with Degeneracy on the Boundary

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Weak solution boundary degeneracy parabolic system initial boundary value problem existence,stability
• 年，卷（期）: 2019,（3）
• 页码范围: 281-292
• 页数: 12页
• 分类号: O175.29|O175.26
• 语种: 英文
• DOI: 10.4208/jpde.v32.n3.5

摘要

In this article,we study the system with boundary degeneracy uit-div(a(x)｜▽ui｜pi-2▽ui) =fi(x,t,u1,u2),(x,t) ∈ΩT.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),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.