On a class of SPDEs called Brownian particle equation model for nonlinear diffusions (Q2732328)
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scientific article; zbMATH DE number 1623586
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a class of SPDEs called Brownian particle equation model for nonlinear diffusions |
scientific article; zbMATH DE number 1623586 |
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3 February 2002
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stochastic partial differential equation
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Gaussian white noise
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Brownian particle equation
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Cauchy problem
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nonlinear diffusion
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method of characteristics
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On a class of SPDEs called Brownian particle equation model for nonlinear diffusions (English)
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The author considers a stochastic partial differential equation (SPDE) of hyperbolic type, that is perturbed by the Gaussian white noise. Such SPDE is called a Brownian particle equation (BPE). A BPE permits to construct a probabilistic solution of parabolic equation, using the method of characteristics. The author investigates how to apply BPE model to nonlinear problems. He constructs the probabilistic solution of the nonlinear diffusion equation and proves some results concerning the Cauchy problem of the nonlinear BPE. Possible applications to the numerical analysis of relevant phenomena are discussed. A BPE model of the reaction-diffusion problem and a method of getting the numerical estimation of the solution are presented.
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