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.

引用

页数：15

共 50 条

[41] An explicit solution of a parabolic equation with nonlocal boundary conditions [J].

Bastys A. ;

Ivanauskas F. ;

Sapagovas M. .

Lithuanian Mathematical Journal, 2005, 45 (3) :257-271

[42] Initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal boundary condition* [J].

Alexander Gladkov .

Lithuanian Mathematical Journal, 2017, 57 :468-478

[43] Determination of the Coefficient of a Semilinear Parabolic Equation for a Boundary-Value Problem with Nonlinear Boundary Condition [J].

Akhundov, A. Ya. ;

Gasanova, A. I. .

UKRAINIAN MATHEMATICAL JOURNAL, 2014, 66 (06) :949-954

[44] Initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal boundary condition* [J].

Gladkov, Alexander .

LITHUANIAN MATHEMATICAL JOURNAL, 2017, 57 (04) :468-478

[45] Determination of the Coefficient of a Semilinear Parabolic Equation for a Boundary-Value Problem with Nonlinear Boundary Condition [J].

A. Ya. Akhundov ;

A. I. Gasanova .

Ukrainian Mathematical Journal, 2014, 66 :949-954

[46] On the stability of the equation with a partial boundary value condition [J].

Huashui Zhan .

Boundary Value Problems, 2018

[47] A new kind of the solution of degenerate parabolic equation with unbounded convection term [J].

Zhan, Huashui .

OPEN MATHEMATICS, 2015, 13 :283-297

[48] Inverse Problem for Degenerate Parabolic-Hyperbolic Equation with Nonlocal Boundary Condition [J].

Sabitov, K. B. ;

Sidorov, S. N. .

RUSSIAN MATHEMATICS, 2015, 59 (01) :39-50

[49] Global existence and blowup for a degenerate parabolic equation with a free boundary [J].

Chen, Youpeng ;

Liu, Xingying .

ANNALES POLONICI MATHEMATICI, 2020, 124 (01) :1-31

[50] The well-posedness of an anisotropic parabolic equation based on the partial boundary value condition [J].

Zhan, Huashui .

BOUNDARY VALUE PROBLEMS, 2017,

← 1 2 3 4 5 →