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RESEARCH PRODUCT

On the relativistic heat equation in one space dimension

José A. CarrilloSalvador MollVicente Caselles

subject

General Mathematics010102 general mathematicsMathematical analysisSpace dimensionGeodetic datumLipschitz continuity01 natural sciences010101 applied mathematicsMathematics - Analysis of PDEsScheme (mathematics)FOS: MathematicsHeat equation0101 mathematicsMathematicsAnalysis of PDEs (math.AP)

description

We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows for analysing further properties of their qualitative behaviour. J.A.C. acknowledges partial support by MINECO project, reference MTM2011-27739-C04-02, by GRC 2009 SGR 345 by the Generalitat de Catalunya, and by the Engineering and Physical Sciences Research Council grant number EP/K008404/1. J.A.C. also acknowledges support from the Royal Society through a Wolfson Research Merit Award. V.C. acknowledges partial support by MINECO project, reference MTM2009-08171, by GRC reference 2009 SGR 773, and by “ICREA Academia” prize for excellence in research funded both by the Generalitat de Catalunya. S.M. acknowledges partial support by MINECO project, reference MTM2012-31103.

yearjournalcountryeditionlanguage
2012-11-27
10.1112/plms/pdt015http://arxiv.org/abs/1211.6313