The Cauchy problem for nonlinear parabolic equations with Levy Laplacian

被引：2

作者：

Albeverio, S

Belopolskaya, Y

Feller, M

机构：

[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

[2] BiBoS, Bielefeld, Germany

[3] CERFIM, Locarno, Switzerland

[4] St Petersburg State Univ Architecture & Civil Eng, St Petersburg 190005, Russia

[5] UkrNIIMOD, UA-03680 Kiev, Ukraine

来源：

POTENTIAL ANALYSIS | 2006年 / 24卷 / 02期

关键词：

Levy Laplacian; nonlinear parabolic equations; the Cauchy problem;

D O I：

10.1007/s11118-005-3886-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A solution to the Cauchy problem for a rather general class of nonlinear parabolic equations involving the infinite-dimensional Laplacian Delta(L) of the form f (U(t, x), partial derivative U(t, x)/partial derivative t, Delta(L)U( t, x)) = 0, where f is a real function defined on R-3 is presented.

引用

页码：125 / 136

页数：12

共 50 条

[1] The Cauchy Problem for Nonlinear Parabolic Equations with Lévy Laplacian
S. Albeverio
Ya. Belopolskaya
M. Feller
Potential Analysis, 2006, 24 : 125 - 136
[2] BOUNDARY PROBLEMS FOR FULLY NONLINEAR PARABOLIC EQUATIONS WITH LEVY LAPLACIAN
Albeverio, S.
Belopolskaya, Ya.
Feller, M.
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2008, 14 (01): : 1 - 9
[3] Cauchy problem for nonlinear parabolic equations with a gradient term
Shang, Haifeng
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (08) : 2801 - 2825
[4] On the Cauchy problem for nonlinear parabolic equations with variable density
Punzo, Fabio
JOURNAL OF EVOLUTION EQUATIONS, 2009, 9 (03) : 429 - 447
[5] On the Cauchy problem for nonlinear parabolic equations with variable density
Fabio Punzo
Journal of Evolution Equations, 2009, 9 : 429 - 447
[6] The Cauchy problem for the wave equation with Levy Laplacian
Albeverio, S. A.
Belopol'skaya, Ya. I.
Feller, M. N.
MATHEMATICAL NOTES, 2010, 87 (5-6) : 787 - 796
[7] Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations
Kazuhiro Ishige
Tatsuki Kawakami
Journal d'Analyse Mathématique, 2013, 121 : 317 - 351
[8] Stochastic Model of the Cauchy–Neumann Problem for Nonlinear Parabolic Equations
Belopolskaya Y.I.
Journal of Mathematical Sciences, 2024, 281 (1) : 24 - 40
[9] Probabilistic Interpretation of the Cauchy Problem for Systems of Nonlinear Parabolic Equations
Belopolskaya, Ya. I.
DIFFERENTIAL EQUATIONS, 2022, 58 (12) : 1590 - 1608
[10] Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations
Qu, Changzheng
Kang, Jing
STUDIES IN APPLIED MATHEMATICS, 2014, 132 (02) : 81 - 111

← 1 2 3 4 5 →