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http://dx.doi.org/10.14403/jcms.2017.30.4.397

EXTINCTION AND POSITIVITY OF SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC EQUATIONS WITH GRADIENT SOURCE TERMS

Yi, Su-Cheol (Department of Mathematics Changwon National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.30, no.4, 2017 , pp. 397-409 More about this Journal

Abstract

In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

Keywords

semilinear parabolic equation; extinction; positivity; decay estimate;

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Reference

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