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arXiv · 1710.06780

Upper bound for lifespan of solutions to certain semilinear parabolic, dispersive and hyperbolic equations via a unified test function method

Masahiro Ikeda·Motohiro Sobajima
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Abstract

This paper is concerned with the blowup phenomena for initial-boundary value problem for certain semi linear parabolic, dispersive and hyperbolic equations in cone-like domain. The result proposes a unified treatment of estimates for lifespan of solutions to the problem by test function method. The Fujita exponent p=1 + 2/N appears as a threshold of blowup phenomena for small data when $C_{{\Sigma}}=R^N$ , but the case of cone-like domain with boundary the threshold changes and explicitly given via the first eigenvalue of corresponding Laplace-Beltrami operator with Dirichlet boundary condition as in Levine-Meier in 1989.

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Masahiro Ikeda, Motohiro Sobajima. 2017-10-18. Upper bound for lifespan of solutions to certain semilinear parabolic, dispersive and hyperbolic equations via a unified test function method. https://arxiv.org/abs/1710.06780

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