Some regularity results on the 'relativistic' heat equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:245

Article

Andreu, F.³  Caselles, V.²  Mazon, J. M.¹ 

[1] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

[2] Univ Pompeu Fabra, Dept Tecnol, Barcelona 08003, Spain

[3] Univ Valencia, Dept Matemat Aplicada, E-46100 Valencia, Spain

关键词: Flux limited diffusion equations;    Entropy solutions;    Heat equation;   

DOI  :  10.1016/j.jde.2008.06.024

来源: Elsevier

【 摘 要 】

We prove some partial regularity results for the entropy solution u of the so-called relativistic heat equation. In particular, under some assumptions on the initial condition u(0), we prove that u(t)(t) is a Radon measure in R-N. Moreover, if u(0) is log-concave inside its support S?, S? being a convex set, then we show the solution u(t) is also log-concave in its support Omega(t). This implies its smoothness in Omega(t). In that case we can give a simpler characterization of the notion of entropy solution. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free