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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Instability of solutions of a semilinear heat equation with a Neumann boundary condition


Authors: Keng Deng and Cheng-Lin Zhao
Journal: Quart. Appl. Math. 63 (2005), 13-19
MSC (2000): Primary 34B18, 35B05, 35B35, 35K60
Published electronically: January 19, 2005
MathSciNet review: 2126566
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Abstract | References | Similar Articles | Additional Information

Abstract: A semilinear heat equation $u_t=u_{xx}+\varepsilon u^p,0<x<1,\ \varepsilon, p>0,$ subject to $u_x(0,t)=0,u_x(1,t)=-u^{-q}(1,t),\ q>0$ is studied. The set of stationary states is characterized, their instability is analyzed, and the large time behavior of positive solutions is discussed.


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Additional Information

Keng Deng
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504

Cheng-Lin Zhao
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504

DOI: http://dx.doi.org/10.1090/S0033-569X-05-00946-2
PII: S 0033-569X(05)00946-2
Received by editor(s): July 24, 2003
Published electronically: January 19, 2005
Additional Notes: The work of the first author was supported in part by the National Science Foundation under grant DMS-0211412
Article copyright: © Copyright 2005 Brown University



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