Renormalized solutions for some nonlinear degenerated parabolic problems
Mohammed EL FATRY, Mounir MEKKOUR, Youssef AKDIM
Received September 8, 2025. Published online June 9, 2026.
Abstract: We prove the existence of a renormalized solution to the problem of the nonlinear degenerate parabolic equation frac{\partial u}{\partial t}-\sum_{i=1}^N\frac{\partial}{\partial x_i}\biggl( \omega_i(x) \sum_{j=1}^Na_{ij}(t,x,u)\frac{\partial u}{\partial x_j}\biggr) =f, where the matrix $A(t,x,s)=(a_{ij}(t,x,s))_{1\leq i,j\leq N}$ is not controlled with respect to $ u $ and $f\in L^1(Q)$.
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