Author(s)

Safimba Soma, Mohamed Bance

Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso.

We consider a class of doubly nonlinear history-dependent problems having a convection term and a pseudomonotone nonlinear diffusion operator associated an equation of the type ?_t(k * (b(v) - b(v₀))) - div(a(x,Dv) + F(v)) = f where the right hand side belongs to L¹. The kernel k belongs to the large class of PC kernels. In particular, the case of fractional time derivatives of order α ∈ (0,1) is included. Assuming b nondecreasing with L¹-data, we prove existence in the framework of entropy solutions. The approach adopted for the proof is based on a several step approximation method and by using a result in the case of a strictly increasing b.

Fractional Time Derivative, Nonlinear Volterra Equation, Doubly Nonlinear, Entropy Solution

Soma, S. and Bance, M. (2023) On Existence of Entropy Solution for a Doubly Nonlinear Differential Equation with L¹ -Data. Journal of Applied Mathematics and Physics, 11, 4092-4127. doi: 10.4236/jamp.2023.1112261.