The partial boundary value conditions of nonlinear degenerate parabolic equation

被引：0
|
作者：
Zhi, Yuan [1 ]
Zhan, Huashui [2 ]
机构：
[1] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China
[2] Xiamen Univ Technol, Sch Math & Stat, Xiamen 361024, Peoples R China
来源：
BOUNDARY VALUE PROBLEMS | 2022年 / 2022卷 / 01期
关键词：
Parabolic equation; n-dimensional cube; Entropy solution; Kruzkov bi-variables method; Submanifold; ENTROPY SOLUTIONS; CAUCHY-PROBLEM; UNIQUENESS; STABILITY;
D O I：
10.1186/s13661-022-01608-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The stability of the solutions to a parabolic equation partial derivative u/partial derivative t = Delta A(u) + Sigma(N)(i=1) b(i)(x, t)D(i)u - c(x, t)u - f (x, t) with homogeneous boundary condition is considered. Since the set {s : A' (s) = a(s) = 0} may have an interior point, the equation is with strong degeneracy and the Dirichlet boundary value condition is overdetermined generally. How to find a partial boundary value condition to match up with the equation is studied in this paper. By choosing a suitable test function, the stability of entropy solutions is obtained by Kruzkov bi-variables method.
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页数：15
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