Random-field solutions of weakly hyperbolic stochastic partial differential equations with polynomially bounded coefficients

被引：7

作者：

Ascanelli, Alessia ^{[1
]}

Coriasco, Sandro ^{[2
]}

Suss, Andre ^{[1
]}

机构：

[1] Univ Ferrara, Dipartimento Matemat Informat, Via Machiavelli 30, I-44121 Ferrara, Italy

[2] Univ Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2020年 / 11卷 / 01期

关键词：

Hyperbolic stochastic partial differential equations; Random-field solutions; Variable coefficients; Fundamental solution; Fourier integral operators; FOURIER INTEGRAL-OPERATORS; CAUCHY-PROBLEM; WAVE-EQUATION; REGULARITY;

D O I：

10.1007/s11868-019-00290-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study random-field solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider linear equations under suitable hyperbolicity hypotheses, and we provide conditions on the initial data and on the stochastic term, namely, on the associated spectral measure, so that these kind of solutions exist in suitably chosen functional classes. We also give a regularity result for the expected value of the solution.

引用

页码：387 / 424

页数：38

共 37 条

[1] Abdeljawad A., 2018, ARXIV181005009
[2] [Anonymous], 1998, Annali dell'Universita di Ferrara
[3] Ascanelli A., 2017, GEN FUNCTIONS FOURIE, P1, DOI [10.1007/978-3-319-51911-1_1, DOI 10.1007/978-3-319-51911-1_1]
[4] Ascanelli A., 2018, ARXIV161001208
[5] Log-Lipschitz regularity for SG hyperbolic systems
Ascanelli, Alessia
Cappiello, Marco
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 230 (02) : 556 - 578
[6] Random-field solutions to linear hyperbolic stochastic partial differential equations with variable coefficients
Ascanelli, Alessia
Suss, Andre
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (08) : 2605 - 2641
[7] Ascanelli A, 2015, J PSEUDO-DIFFER OPER, V6, P521, DOI 10.1007/s11868-015-0132-x
[8] Ascanelli A, 2010, OSAKA J MATH, V47, P423
[9] Billingsley P., 1995, PROBABILITY MEASURE
[10] Cicognani M, 1997, B UNIONE MAT ITAL, V11B, P643

← 1 2 3 4 →