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Life span and a new critical exponent for a doubly degenerate parabolic equation with slow decay initial values. (English) Zbl 1227.35053
Summary: We investigate the behavior of the positive solution of the Cauchy problem for the equation $$u_t- \text{div}\big(|\nabla u^m|^{p-2}\nabla u^m\big)=u^q$$ with initial value decaying at infinity, and give a new secondary critical exponent for the existence of global and nonglobal solutions. Furthermore, the large time behavior and the life span of solutions are also studied.

35B33Critical exponents (PDE)
35B44Blow-up (PDE)
35K65Parabolic equations of degenerate type
35K59Quasilinear parabolic equations
Full Text: DOI
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