Removability conditions for anisotropic parabolic equations in a computational validation

Abstract

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The article investigates removability conditions for singularities of anisotropic parabolic equations and in particular for the anisotropic porous medium equation and it aims in the numerical validation of the analytical results. The preconditions on the strength of the anisotropy are analyzed, and the analytical estimates for the growth behavior of the solutions near the singularities are compared with the observed growth in numerical simulations. Despite classical estimates used in the proof, we find that the analytical estimates are surprisingly close to the numerically observed solution behavior.

Keywords

• parabolic differential equation
• anisotropic porous medium equation
• anisotropic fast diffusion equation
• removable singularity
• removability conditions
• numerical validation