Asymptotic and other estimates for semilinear parabolic problem in semi-infinite cylinder |
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Authors: | J C Song |
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Institution: | Department of Applied Mathematics, Hanyang University, Ansan, Gyeonggido 426791, Korea |
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Abstract: | The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder
of variable cross-section subject to zero condition on the lateral boundaries is investigated. A second-order differential
inequality that shows the spatial decay O(exp(−z
2/(4(t+t
0)))) for an L
2p
cross-sectional measure of the solution is obtained. A first-order differential inequality leading to growth or decay is
also derived. In the case of growth, an upper bound for blow-up in space is obtained, while in the case of decay an upper
bound for the total energy in terms of data is obtained. |
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Keywords: | spatial decay bound differential inequality decay rate |
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