A fundamental question for any PDE is the existence and uniqueness of a solution for given boundary conditions. For nonlinear equations these questions are in general very hard, hence we need an answer for the above question . Thank you very much!
Kabir Sadeghi
The answer is a little long and complicated, I recommend you read about
entropy solution, normalized solution and weak solution for a nonlinear parabolic equation in a paper by clicking the following link:
Article Renormalized and entropy solutions of nonlinear parabolic system
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