Nonlinear stochastic wave and heat equations

被引：111

作者：

Peszat, S

Zabczyk, J

机构：

[1] Polish Acad Sci, Inst Math, PL-31027 Krakow, Poland

[2] Polish Acad Sci, Inst Math, PL-00950 Warsaw, Poland

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2000年 / 116卷 / 03期

关键词：

stochastic wave and heat equations; homogeneous Wiener process;

D O I：

10.1007/s004400050257

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study nonlinear wave and heat equations on R-d driven by a spatially homogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary R-d-space. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.

引用

页码：421 / 443

页数：23

共 20 条

[1] Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process [J].

Brzezniak, Z ;

Peszat, S .

STUDIA MATHEMATICA, 1999, 137 (03) :261-299

[2]

Da Prato G, 1996, ERGODICITY INFINITE

[3]

Da Prato G, 1992, STOCHASTIC EQUATIONS

[4]

Dalang RC, 1998, ANN PROBAB, V26, P187

[5]

Dalang RC., 1999, Electron. J. Probab, V4, P6

[6] SPATIALLY HOMOGENEOUS RANDOM EVOLUTIONS [J].

DAWSON, DA ;

SALEHI, H .

JOURNAL OF MULTIVARIATE ANALYSIS, 1980, 10 (02) :141-180

[7]

FUNAKI T, 1991, OSAKA J MATH, V28, P495

[8]

GAVEAU B, 1995, B SCI MATH, V119, P381

[9]

Gelfand I. M., 1964, Applications of harmonic analysis, VIV

[10]

ITO K, 1984, FDN STOCHASTIC DIFFE

← 1 2 →