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Zimmermann, A. (2010) Renormalized Solutions for Nonlinear Partial Differential Equations with Variable Exponents and L1-Data. PhD Thesis, Fakultät II: Mathematik und Naturwissenschaften, Berlin.

has been cited by the following article:

• 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.