Self-Similar Solutions of the Cauchy Problem for a Parabolic Stochastic Differential Equation

The dynamics of stochastic nonlinear parabolic equations is analyzed. Self-similar solutions of the Cauchy problem for a quasilinear stochastic equation of the parabolic type with power-law nonlinearities are constructed. The dynamics of the solutions and their supports is studied with the use of co...

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Bibliographic Details
Published in:	Differential equations Vol. 55; no. 8; pp. 1077 - 1083
Main Author:	Mel’nik, S. A.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-08-2019 Springer Springer Nature B.V
Subjects:	Cauchy problems Difference and Functional Equations Differential equations Mathematics Mathematics and Statistics Nonlinear analysis Nonlinear dynamics Nonlinear equations Ordinary Differential Equations Partial Differential Equations Self-similarity
Online Access:	Get full text
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Summary:	The dynamics of stochastic nonlinear parabolic equations is analyzed. Self-similar solutions of the Cauchy problem for a quasilinear stochastic equation of the parabolic type with power-law nonlinearities are constructed. The dynamics of the solutions and their supports is studied with the use of comparison theorems.
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266119080081