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Mathematics of the USSR-Sbornik, 1989, Volume 62, Issue 2, Pages 525–539
DOI: https://doi.org/10.1070/SM1989v062n02ABEH003252
(Mi sm3023)
 

Branching diffusion processes and systems of reaction-diffusion differential equations

R. G. Safaryan
References:
Abstract: Systems of reaction-diffusion differential equations of the form
ukt=Lkuk+fk(t,x,u),xDRr, t>0, u=(u1,,un),1kn,
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
Bibliographic databases:
UDC: 519.21
MSC: Primary 60J80, 60J60, 35K57; Secondary 35K05, 35K65
Language: English
Original paper language: Russian
Citation: R. G. Safaryan, “Branching diffusion processes and systems of reaction-diffusion differential equations”, Math. USSR-Sb., 62:2 (1989), 525–539
Citation in format AMSBIB
\Bibitem{Saf87}
\by R.~G.~Safaryan
\paper Branching diffusion processes and systems of reaction-diffusion differential equations
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 2
\pages 525--539
\mathnet{http://mi.mathnet.ru//eng/sm3023}
\crossref{https://doi.org/10.1070/SM1989v062n02ABEH003252}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=933701}
\zmath{https://zbmath.org/?q=an:0663.60066}
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    References:54
     
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