Asymptotic and Other Estimates for a Semilinear Parabolic Problem in a Semi-Infinite Cylinder

J. C. Song

doi:10.3879/j.issn.1000-0887.2011.10.009

Volume 32 Issue 10

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J. C. Song. Asymptotic and Other Estimates for a Semilinear Parabolic Problem in a Semi-Infinite Cylinder[J]. Applied Mathematics and Mechanics, 2011, 32(10): 1241-1246. doi: 10.3879/j.issn.1000-0887.2011.10.009

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Asymptotic and Other Estimates for a Semilinear Parabolic Problem in a Semi-Infinite Cylinder

doi: 10.3879/j.issn.1000-0887.2011.10.009

J. C. Song

Department of Applied Mathematics, Hanyang University, Ansan, Gyeonggido 426-791, Korea

Received Date: 2010-10-11
Rev Recd Date: 2011-07-13
Publish Date: 2011-10-15

Abstract

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 was investigated.A second-order differential inequality that was to show the spatial decay O(exp{-z²/[4(t+t₀)]}) for an L^2p cross-sectional measure of the solution was obtained.A first-order differential inequality leading to growth or decay was derived.In the case of growth an upper bound for blow-up in space was obtained while in the case of decay an upper bound for the total energy in terms of data was obtained.
- spatial decay bound,
- differential inequality,
- decay rate

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References(8)

References

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