Existence solutions for a class of nonlinear parabolic equations with variable exponents and L^1 data

Abstract

In this article, we study the problem
 (∂ b(x,u) ∕ ∂ t) - div a(x, t, u, ∇ u) + div φ(u) = f, in Ω × ]0, T],
 u = 0 on ∂ Ω × ]0,T[
 b(x,u)(t=0) = b(x,u0). in Ω,
 in the framework of generalized Sobolev spaces, with b(x,u) unbounded function on u. The main contribution of our work is to prove the existence of renormalized solutions when the second term f belongs to L1(QT).

Existence and uniqueness of renormalized solutions to nonlinear multivalued parabolic problem with homogeneous Dirichlet boundary conditions involving variable exponent

“…For other works in this direction, see [11,16]. The aim of our paper is to extend the results in [10] , to the case of a monotone graph β instead of a continuous and monotone function b.…”

Global existence of a pair of coupled Cahn-Hilliard equations with nondegenerate mobility and logarithmic potential

“…For investigations into fourth-order degenerate parabolic equations in one spatial dimension, refer to the work in [8]. Given the significance of this topic, recent studies have delved into the existence and uniqueness of differential equations, as evidenced in [3,4,5,16,21,25,27,31,32,33,37].…”