Explicit solutions to dynamic diffusion-type equations and their time integrals

This paper deals with solutions of diffusion-type partial dynamic equations on discrete-space domains. We provide two methods for finding explicit solutions, examine their asymptotic behavior and time integrability. These properties depend significantly not only on the underlying time structure but...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-05, Vol.234, p.486-505
Main Authors: Slavik, Antonin, Stehlik, Petr
Format: Article
Language:English
Subjects:
Asymptotic properties
Diffusion
Diffusion equation
Dynamics
Heat equation
Integrals
Mathematical analysis
Mathematical models
Partial dynamic equations
Random walk
Semidiscrete equations
Stochastic processes
Symmetry
Time scales
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Summary:This paper deals with solutions of diffusion-type partial dynamic equations on discrete-space domains. We provide two methods for finding explicit solutions, examine their asymptotic behavior and time integrability. These properties depend significantly not only on the underlying time structure but also on the dimension and symmetry of the problem. Throughout the paper, the results are interpreted in the context of random walks and related stochastic processes.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.01.176