Nonlinear evolution equations with gradient coupled noise

被引：5

作者：

Benth, FE ^{[1
]}

Deck, T

Pothoff, J

Streit, L

机构：

[1] Univ Oslo, N-0316 Oslo, Norway

[2] Univ Mannheim, D-68131 Mannheim, Germany

[3] Univ Bielefeld, BiBoS, D-33615 Bielefeld, Germany

[4] Univ Madeira, P-9000 Funchal, Portugal

来源：

LETTERS IN MATHEMATICAL PHYSICS | 1998年 / 43卷 / 03期

关键词：

Burgers equation; Korteweg-de Vries equation;

D O I：

10.1023/A:1007456027371

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show existence and uniqueness of solutions for a class of nonlinear evolution equations with gradient coupled noise. Our results are obtained by using a simple transformation relating the equation under consideration to an underlying deterministic partial differential equation. Both the It (o) over cap and the Stratonovich conventions are treated. Several examples show that the properties of solutions for It (o) over cap equations can differ significantly from those of Stratonovich equations.

引用

下载

页码：267 / 278

页数：12

共 50 条

[31] ON NONLINEAR EQUATIONS OF EVOLUTION
CRANDALL, MG
SOUGANIDIS, PE
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1989, 13 (12) : 1375 - 1392
[32] NONLINEAR EQUATIONS OF EVOLUTION
CALVERT, BD
PACIFIC JOURNAL OF MATHEMATICS, 1971, 39 (02) : 293 - &
[33] Nonlinear Evolution Equations
Precup, Radu
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2006, 51 (01): : 135 - 136
[34] Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions
Toelle, Jonas M.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 130 (05) : 3220 - 3248
[35] SPECIAL SOLUTIONS OF COUPLED NONLINEAR EVOLUTION EQUATIONS WITH BUMPS THAT BEHAVE AS INTERACTING PARTICLES
CALOGERO, F
DEGASPERIS, A
LETTERE AL NUOVO CIMENTO, 1977, 19 (14): : 525 - 533
[36] On coupled envelope evolution equations in the Hamiltonian theory of nonlinear surface gravity waves
Li, Yan
JOURNAL OF FLUID MECHANICS, 2023, 960
[37] Hybrid rogue wave and breather solutions for the nonlinear coupled dispersionless evolution equations
Dong, Hao-Nan
Zhaqilao
WAVE MOTION, 2024, 125
[38] A Meshless Method of Lines for Numerical Solution of Some Coupled Nonlinear Evolution Equations
Ali, Arshed
Haq, Fazal
Hussain, Iltaf
Shah, Usman
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2014, 15 (02) : 121 - 128
[39] Stabilization of evolution equations by noise
Kwiecinska, AA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (10) : 3067 - 3074
[40] Gradient regularity for nonlinear parabolic equations
Kuusi, Tuomo
Mingione, Giuseppe
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2013, 12 (04) : 755 - 822

← 1 2 3 4 5 →