Blow up behavior for a semilinear parabolic equation with localized source |
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Authors: | Ming Yang Hui-ling Li |
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Affiliation: | Department of Mathematics, Southeast University, Nanjing, 210096, China |
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Abstract: | In this paper, we investigate the blow-up behavior of solutions of a parabolic equation with localized reactions. We completely classify blow-up solutions into the total blow-up case and the single point blow-up case, and give the blow-up rates of solutions near the blow-up time which improve or extend previous results of several authors. Our proofs rely on the maximum principle, a variant of the eigenfunction method and an initial data construction method. |
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Keywords: | semilinear parabolic equation single point blow-up total blow-up blow up rate localized source |
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