Geodesic
A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel
Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1263-1275

Voir la notice de l'article provenant de la source Cambridge University Press

We give a modulus of continuity for solutions of the wave equation with a noise term:utt = Δu + a(u) + b(u)G, x ∈ R3where G is a Gaussian noise. This case is more difficult than in lower dimensions because the fundamental solution of the wave equation is singular.
DOI : 10.4153/CJM-1993-071-7
Mots-clés : 60H15, 35R60, 35L05 
Mueller, C. A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel. Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1263-1275. doi: 10.4153/CJM-1993-071-7
@article{10_4153_CJM_1993_071_7,
     author = {Mueller, C.},
     title = {A {Modulus} for the {3-Dimensional} {Wave} {Equation} {With} {Noise:} {Dealing} {With} a {Singular} {Kernel}},
     journal = {Canadian journal of mathematics},
     pages = {1263--1275},
     year = {1993},
     volume = {45},
     number = {6},
     doi = {10.4153/CJM-1993-071-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-071-7/}
}
TY  - JOUR
AU  - Mueller, C.
TI  - A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel
JO  - Canadian journal of mathematics
PY  - 1993
SP  - 1263
EP  - 1275
VL  - 45
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-071-7/
DO  - 10.4153/CJM-1993-071-7
ID  - 10_4153_CJM_1993_071_7
ER  - 
%0 Journal Article
%A Mueller, C.
%T A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel
%J Canadian journal of mathematics
%D 1993
%P 1263-1275
%V 45
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-071-7/
%R 10.4153/CJM-1993-071-7
%F 10_4153_CJM_1993_071_7

[1] 1. Carmona, R. and Nualart, D. (1988a), Random non-linear wave equations: Smoothness of the solution, Prob. Th. Rel. Fields 79, 464–508. Google Scholar

[2] 2. Carmona, R. and Nualart, D. (1988b), Random non-linear wave equations: Propagation of singularities, Ann. Prob. (2) 16, 730–751. Google Scholar

[3] 3. Mueller, C. (1990a), Limit results for two stochastic partial differential equations, Stochastics 37, 175–199. Google Scholar

[4] 4. Mueller, C. (1990b), On the support of solutions to the heat equation with noise, Stochastics, to appear. Google Scholar

[5] 5. Mueller, C. (1990c), Long time existence for the heat equation with a noise term, Prob. Th. Rel. Fields, to appear. Google Scholar

[6] 6. Mueller, C. (1991), Long time existence for the wave equation with a noise term, Submitted to Ann. Prob. Google Scholar

[7] 7. Sowers, R. (1990a), Large deviations for a reaction-diffusion equation with non-Gaussian perturbations, Ann. Prob., to appear. Google Scholar

[8] 8. Sowers, R. (1990b), Large deviations for the invariant measure of a reaction-diffusion equation with non- Gaussian perturbations, Sub Google Scholar

[9] 9. Treves, F. (1975), Basic Linear Partial Differential Equations, Academic Press, New York. Google Scholar

[10] 10. Walsh, J.B. (1984), An introduction to stochastic partial differential equations, École d'Été de Probabilités de Saint-Fleur, XIV, Lect. Notes Math. 1180, Springer, New York Google Scholar

Cité par Sources :