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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.

MSC:

35K65 Degenerate parabolic equations
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