The limit of vanishing viscosity for doubly nonlinear parabolic equations

Abstract

We show that solutions of the doubly nonlinear parabolic equation ∂b(u) ∂t − e div(a(∇u)) + div( f (u)) = g converge in the limit e ↘ 0 of vanishing viscosity to an entropy solution of the doubly nonlinear hyperbolic equation ∂b(u) ∂t + div( f (u)) = g . The difficulty here lies in the fact that the functions a and b specifying the diffusion are nonlinear. 

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