Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems. (English) Zbl 0932.35129

The paper is devoted to uniqueness and a comparison principle in \(L^1\) for renormalized solutions for the degenerate elliptic-parabolic equation \[ b(u)_t= \text{div }a(u,Du)+ f, \] where \(a\) is a continuous vector field satisfying a growth condition. The authors explain the correspondence between weak and renormalized solutions. To prove their results, they use Kruzhkov’s method of doubling variables both in space and time.


35K65 Degenerate parabolic equations
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