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On a general approach to extinction and blow-up for quasi-linear heat equations. (English. Russian original) Zbl 0823.35085
Comput. Math. Math. Phys. 33, No. 2, 217-227 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 2, 246-258 (1993).
Summary: An investigation is made of the asymptotic behaviour of nonnegative solutions \(u= u(| x|,t)\) of the heat-conduction equation of general form with heat source or sink \(u_ t= \Delta\varphi (u)\pm Q(u)\), where \(\varphi'\) and \(Q\) are given nonnegative functions. It is shown that, by careful application of the Friedman-McLeod method, asymptotic estimates can be obtained for the solutions near the blow-up or extinction times which, it is established, are exact for \(\varphi\) and \(Q\) of certain special forms.

35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs