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On the problem of preventing blowing-up and quenching for semilinear heat equation

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Abstract

In this paper, the global existence of solutions to the IVP

$$ = \Delta u + g(t)f(u) (t > 0), \left. u \right|_{1 - 0} = u_0 (x)$$

and the IBVP

$$u_1 = \Delta u + g(t,x)f(u) (t > 0, x \in \Omega ), \left. u \right|_{1 - 0} = \left. u \right|_{\partial O} = 0$$

is investigated. As has been done in [6], the introduction of factor g(t) or g(t, x) in nonlinear term is to prevent the occurrance of blowing-up or quenching of solutions. It is shown in this paper that most of the restrictions on f. g and uo, in the theorems of [6] may be cancelled or relaxed, that the smallness of g is required only for t large, and that under certain conditions controlling initial state can avoid blowing-up.

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Authors and Affiliations

  1. Department of Mathematics, Jilin University, Jilin

    Yan Zi-qian

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  1. Yan Zi-qian
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Zi-qian, Y. On the problem of preventing blowing-up and quenching for semilinear heat equation. Appl Math Mech 7, 767–773 (1986). https://doi.org/10.1007/BF01900609

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  • DOI: https://doi.org/10.1007/BF01900609

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