Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Convergence rate to the singular solution for the Gelfand equation and its stability


Author: Sun-Ho Choi
Journal: Quart. Appl. Math. 72 (2014), 773-797
MSC (2010): Primary 34D23
DOI: https://doi.org/10.1090/S0033-569X-2014-01370-4
Published electronically: November 7, 2014
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Abstract: We study the asymptotic behaviors of the solution to the Gelfand equation. The Gelfand equation appears in the kinetic theory of gravitational steady state and the theory of nonlinear diffusion. We present a convergence rate of the solutions of the Gelfand equation to the unique singular solution as $ r$ goes to infinity and prove asymptotic stability of the solution by considering the initial value problem for the Gelfand equation. To obtain the convergence rate and the point-wise stability estimate, we construct a uniform lower bound function and use the solution for the linearized Gelfand equation.


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Additional Information

Sun-Ho Choi
Affiliation: Department of Mathematical Sciences, KAIST, Daejeon 305-701, Republic of Korea
Email: lpgilin@gmail.com

DOI: https://doi.org/10.1090/S0033-569X-2014-01370-4
Received by editor(s): February 15, 2013
Published electronically: November 7, 2014
Article copyright: © Copyright 2014 Brown University


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