The Cauchy problem for a class of quasilinear parabolic equations

被引：1

作者：

Alkis S. Tersenov

Aris S. Tersenov

机构：

[1] University of Crete,Department of Mathematics

[2] FO.R.T.H.,Institute of Appl. and Comp. Mathematics

来源：

Annali di Matematica Pura ed Applicata | 2003年 / 182卷 / 3期

关键词：

quasilinear parabolic equations; Hamilton–Jacobi equation;

D O I：

10.1007/s10231-002-0070-0

中图分类号：

学科分类号：

摘要：

The present paper is concerned with the Cauchy problem for the parabolic equation ut+H(t,x,u,∇u)=εΔu. New conditions guaranteeing the global classical solvability are formulated. Moreover, it is shown that the same conditions guarantee the global existence of the Lipschitz continuous viscosity solution for the related Hamilton–Jacobi equation.

引用

页码：325 / 336

页数：11

共 50 条

[1] On Stabilization of the Solution of the Cauchy Problem for Quasilinear Parabolic Equations
V. N. Denisov
A. B. Muravnik
[J]. Differential Equations, 2002, 38 : 369 - 374
[2] On stabilization of the solution of the Cauchy problem for quasilinear parabolic equations
Denisov, VN
Muravnik, AB
[J]. DIFFERENTIAL EQUATIONS, 2002, 38 (03) : 369 - 374
[3] A remark on the global solvability of the Cauchy problem for quasilinear parabolic equations
Tersenov, AS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 260 (01) : 46 - 54
[4] CAUCHY-PROBLEM FOR A CLASS OF QUASILINEAR ULTRAPARABOLIC EQUATIONS
CHOBANOV, GI
[J]. DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 1975, 28 (12): : 1579 - 1581
[5] Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations
ZHAO Junning & ZHAN Huashui Department of Mathematics
[J]. Science China Mathematics, 2005, (05) : 583 - 593
[6] Cauchy Problem for Autonomous Quasilinear Parabolic Pseudodifferential Equations with Deviating Argument
Drin' Y.M.
Petryshyn R.I.
[J]. Journal of Mathematical Sciences, 2014, 197 (1) : 29 - 38
[7] Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations
Junning Zhao
Huashui Zhan
[J]. Science in China Series A: Mathematics, 2005, 48 : 583 - 593
[8] Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations
Zhao, JN
Zhan, HS
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2005, 48 (05): : 583 - 593
[9] CAUCHY PROBLEM IN QUASILINEAR PARABOLIC DIFFERENTIAL EQUATIONS WITH UNSTEADY INITIAL VALUES
SCHLEINKOFER, G
[J]. MATHEMATISCHE ANNALEN, 1971, 191 (04) : 337 - +
[10] Propagation of perturbation in a singular Cauchy problem for degenerate quasilinear parabolic equations
Shishkov, AE
[J]. SBORNIK MATHEMATICS, 1996, 187 (9-10) : 1391 - 1410

← 1 2 3 4 5 →