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Branching diffusion processes and systems of reaction-diffusion differential equations
R. G. Safaryan
Abstract:
Systems of reaction-diffusion differential equations of the form
∂uk∂t=Lkuk+fk(t,x,u),x∈D⊆Rr, t>0, u=(u1,…,un),1⩽k⩽n,
are considered. Under certain special conditions on the nonlinear terms fk the solutions of the Cauchy problem and of mixed problems for systems of the type (1) have a representation in the form of an average value of a suitable functional of the sample paths of a corresponding branching process with diffusion. This representation is given, and it is used together with a direct probability investigation of the branching process with diffusion to obtain results on the behavior of solutions of certain problems with a small parameter for systems of the type (1).
Bibliography: 12 titles.
Received: 23.04.1986
Citation:
R. G. Safaryan, “Branching diffusion processes and systems of reaction-diffusion differential equations”, Math. USSR-Sb., 62:2 (1989), 525–539
Linking options:
https://www.mathnet.ru/eng/sm3023https://doi.org/10.1070/SM1989v062n02ABEH003252 https://www.mathnet.ru/eng/sm/v176/i4/p530
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Abstract page: | 314 | Russian version PDF: | 107 | English version PDF: | 15 | References: | 54 |
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