Asymptotic behaviour for logarithmic diffusion
Résumé
In the paper, we prove that the solutions of the $d$-dimensional logarithmic diffusion equation, with non-homogeneous Dirichlet boundary data, decay exponentially in time towards its own steady state. The result is valid not only in $L^1$-norm (as customary when applying entropy dissipation methods), but also in any $L^p$-norm with $p\in [1,+\infty)$.
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