Multidimensional Reaction-Diffusion Equations with White Noise Boundary Perturbations
Sowers, R. B.
Ann. Probab., Tome 22 (1994) no. 4, p. 2071-2121 / Harvested from Project Euclid
In this paper we study multidimensional stochastic reaction-diffusion equations (SRDE's) with white noise boundary data. More precisely, we consider a general SRDE with Robin data to be a white noise field. Because this boundary data is very irregular, we formulate a set of conditions that a random field must satisfy to solve the SRDE. We show that a unique solution exists, and we study the boundary-layer behavior of the solution. This boundary-layer analysis reveals some natural restrictions on the reaction term of the SRDE that ensure that the reaction term does not qualitatively affect the boundary layer. The boundary-layer analysis also leads to the definition of some functional Banach spaces into which are encoded the boundary-layer degeneracies and that would be the natural settings for other analyses of the SRDE of this paper (e.g., large deviations and central limit theorems, approximation theorems).
Publié le : 1994-10-14
Classification:  Stochastic partial differential equations,  reaction-diffusion equations,  Robin problem,  60H15,  35K57,  58G32,  35R60
@article{1176988495,
     author = {Sowers, R. B.},
     title = {Multidimensional Reaction-Diffusion Equations with White Noise Boundary Perturbations},
     journal = {Ann. Probab.},
     volume = {22},
     number = {4},
     year = {1994},
     pages = { 2071-2121},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988495}
}
Sowers, R. B. Multidimensional Reaction-Diffusion Equations with White Noise Boundary Perturbations. Ann. Probab., Tome 22 (1994) no. 4, pp.  2071-2121. http://gdmltest.u-ga.fr/item/1176988495/