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Linear behaviour of solutions of a superlinear heat equation. (English) Zbl 1263.35137
Summary: We give sufficient conditions which guarantee that solutions of a superlinear heat equation decay to zero at the same rate as the solutions of the linear heat equation with the same initial data. This improves a previous result of T.-Y. Lee and W.-M. Ni [Trans. Am. Math. Soc. 333, No. 1, 365–378 (1992; Zbl 0785.35011)] by showing that this behaviour holds for a significantly larger, and rather tightly defined class of solutions.

MSC:
35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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