Asymptotic behaviour for logarithmic diffusion

Francesco Salvarani (1)

1 Dipartimento di matematica F. Casorati

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 $p\in [1,+\infty)$.

Domaines: Equations aux dérivées partielles [math.AP]

Francesco Salvarani. Asymptotic behaviour for logarithmic diffusion. 2009. ⟨hal-00375063v2⟩