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arXiv · 1802.09570

Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint

Goro Akagi·Stefano Melchionna
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Abstract

The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage Mechanics, is reformulated as a mixed form of two different types of doubly nonlinear evolution equations. Global (in time) solutions to some approximate problems are constructed by performing a time discretization argument and by taking advantage of energy techniques based on specific structures of the equation. Moreover, a variational comparison principle for (possibly non-unique) approximate solutions is established and it also enables us to obtain a local solution as a limit of approximate ones.

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Goro Akagi, Stefano Melchionna. 2018-02-26. Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint. https://arxiv.org/abs/1802.09570

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