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Life span and a new critical exponent for a degenerate parabolic equation. (English) Zbl 1066.35047
Summary: We consider the positive solution of the Cauchy problem for the equation $$u_t=u^p\Delta u+u^q,\quad p>1,\ q>1$$ and give a secondary critical exponent of the behavior of initial value at infinity for the existence of global and nonglobal solutions of the Cauchy problem. Furthermore, the life span of solutions are also studied.

MSC:
35K65Parabolic equations of degenerate type
35K55Nonlinear parabolic equations
35K15Second order parabolic equations, initial value problems
35B33Critical exponents (PDE)
35B40Asymptotic behavior of solutions of PDE
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