Search results for "Flux limited diffusion equations"

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A Fisher–Kolmogorov equation with finite speed of propagation

2010

Abstract In this paper we study a Fisher–Kolmogorov type equation with a flux limited diffusion term and we prove the existence and uniqueness of finite speed moving fronts and the existence of some explicit solutions in a particular regime of the equation.

Entropy solutionsPartial differential equationDiffusion equationApplied MathematicsMathematical analysisFlux limited diffusion equationsReaction–diffusion equationsFront propagationReaction–diffusion systemFisher–Kolmogorov equationFokker–Planck equationUniquenessDiffusion (business)Convection–diffusion equationAnalysisMathematicsJournal of Differential Equations
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Some regularity results on the ‘relativistic’ heat equation

2008

AbstractWe 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 u0, we prove that ut(t) is a Radon measure in RN. Moreover, if u0 is log-concave inside its support Ω, Ω being a convex set, then we show the solution u(t) is also log-concave in its support Ω(t). This implies its smoothness in Ω(t). In that case we can give a simpler characterization of the notion of entropy solution.

Flux limited diffusion equationsEntropy solutionsApplied MathematicsHeat equationMathematical analysisRadon measureConvex setInitial value problemHeat equationAnalysisMathematicsJournal of Differential Equations
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