Mathematical Models of Generalized Diffusion

descriptionPublicationkeyboard_double_arrow_right Article 01 May 2001 Brazil Publisher:IOP PublishingJournal:Physica Scripta, volume 63, pages 353-356 (issn: 0031-8949, eissn: 1402-4896,

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Authors: Kraenkel, Roberto André; Senthilvelan, M.;

doi: 10.1238/physica.regular.063a00353

handle: 11449/23488

Mathematical Models of Generalized Diffusion

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Abstract

Summary: The authors discuss equations describing processes involving nonlinear and higher-order diffusion. They focus on a particular case \((u_t=2\lambda_2(uu_x)_x+\lambda_2u_{xxxx})\), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks.

Country

Brazil

Related Organizations

Sao Paulo State University
Brazil
Universidade Estadual Paulista - UNESP
Brazil

Keywords

Diffusion, KdV equations (Korteweg-de Vries equations), self-similar solutions, nonlinear and higher-order diffusion, diffusive shocks, Shock waves and blast waves in fluid mechanics

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