Local Entropy Solution of a Convection-Diffusion Type Integro-Differential Equation

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Résumé

In this work, we prove existence local entropy solution of a convection-diffusion type integro-differential equation
∂t k ∗( j(v)−j(v0)) −∇· a(x,∇ϕ(v)) + F(ϕ(v))= f
in QT := (0,T) ×Ω with Dirichlet boundary condition v(0,
·)= v0 in Ω and L1-data f ∈L1((0,T) ×Ω), j(v0) ∈L1(Ω). To
that end, regularising the data by L∞-functions, using the existence result of entropy solution for these more approximate
data and a comparison and diagonal principle of the regularised entropy solution, we prove the existence of an local
entropy solution.

Mots-clés

fractional time derivative, Nonlinear Volterra equation, Doubly nonlinear, Entropy solution