Convergence of the 'relativistic' heat equation to the heat equation as c → ∞

• Autores: Vicent Caselles Costa
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 51, Nº 1, 2007, págs. 121-142
• Idioma: inglés
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• Resumen

  • We prove that the entropy solutions of the so-called relativistic heat equation converge to solutions of the heat equation as the speed of light $c$ tends to $\infty$ for any initial condition $u_0 \geq 0$ in $L^1(\mathbb{R}^N)\cap L^\infty(\mathbb{R}^N)$.