The partial boundary value conditions of nonlinear degenerate parabolic equation

Boundary Value Problems

卷:2022

Huashui Zhan¹  Yuan Zhi² 

[1] School of Mathematics and Statistics, Xiamen University of Technology;

[2] School of Sciences, Jimei University;

关键词: Parabolic equation;    n-dimensional cube;    Entropy solution;    Kruzkov bi-variables method;    Submanifold;   

DOI  :  10.1186/s13661-022-01608-y

来源: DOAJ

【 摘 要 】

Abstract The stability of the solutions to a parabolic equation ∂ u ∂ t = Δ A ( u ) + ∑ i = 1 N b i ( x , t ) D i u − c ( x , t ) u − f ( x , t ) $$ \frac{\partial u}{\partial t} = \Delta A(u) +\sum_{i=1}^{N}b_{i}(x,t)D_{i}u-c(x,t)u-f(x,t) $$ with homogeneous boundary condition is considered. Since the set { s : A ′ ( s ) = a ( s ) = 0 } $\{s: A'(s)=a(s)=0\}$ 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.

【 授权许可】

Unknown