TITLE:
On Existence of Entropy Solution for a Doubly Nonlinear Differential Equation with L1 -Data
AUTHORS:
Safimba Soma, Mohamed Bance
KEYWORDS:
Fractional Time Derivative, Nonlinear Volterra Equation, Doubly Nonlinear, Entropy Solution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.12,
December
29,
2023
ABSTRACT: 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.