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arXiv · 2309.05023

Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations

Eurica Henriques·Simone Ciani
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Abstract

In this work we are interested in the study of a class of anisotropic porous medium-type equations whose prototype is \[ u_t =\sum_{i=1}^N \left( m_i u^{m_i-1} u_{x_i} \right)_{x_i} \ , \qquad 0<m_1 \leq \cdots \leq m_N <1 \ , \] for which we derive several estimates, namely two Harnack-type inequalities; and, when considering the associated Dirichlet problem, we determine the finite time of extinction and thereby present a decay rate of extinction.

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Eurica Henriques, Simone Ciani. 2023-09-10. Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations. https://arxiv.org/abs/2309.05023

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