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Global existence and non-existence for the degenerate and uniformly parabolic equations with gradient term. (English) Zbl 1295.35294

Summary: We study the Cauchy problem for the degenerate and uniformly parabolic equations with gradient term. The local existence, global existence and non-existence of solutions are obtained. In the case of global solvability, we get the exact estimates of a solution. In particular, we obtain the global existence of solutions in the limiting case.

MSC:

35K92 Quasilinear parabolic equations with \(p\)-Laplacian
35K65 Degenerate parabolic equations
35B44 Blow-up in context of PDEs
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