Blow-up solutions in one-dimensional diffusion models

Blow-up solutions in one-dimensional diffusion models

A sufficient and necessary condition for the existence of blow-up solutions of a certain class of nonlinear Volterra integral equations with kernels arising from various diffusion models and with nonlinearities satisfying the condition g(0)=0 is given in the form of the so-called generalized Osgood...

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Veröffentlicht in:Nonlinear analysis 2014-01, Vol.95, p.632-638
1. Verfasser: MaAolepszy, Tomasz
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Sprache:eng
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Blow-up solutions
Diffusion
Fractional diffusion models
Volterra integral equation
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description A sufficient and necessary condition for the existence of blow-up solutions of a certain class of nonlinear Volterra integral equations with kernels arising from various diffusion models and with nonlinearities satisfying the condition g(0)=0 is given in the form of the so-called generalized Osgood condition. Such nonlinearities were not permitted in the original articles of Olmstead and Roberts where these diffusion models were introduced.
doi_str_mv 10.1016/j.na.2013.10.005
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subjects Blow-up solutions
Diffusion
Fractional diffusion models
Volterra integral equation
title Blow-up solutions in one-dimensional diffusion models
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