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

Author(s): Keng Deng; Cheng-Lin Zhao
Journal: Quart. Appl. Math. 63 (2005), 13-19.
MSC (2000): Primary 34B18, 35B05, 35B35, 35K60
Posted: January 19, 2005
Retrieve article in: PDF DVI PostScript

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.

References:

1.
K. Deng and M. Xu, Quenching for a nonlinear diffusion equation with a singular boundary condition, Z. Angew. Math. Phys. 50 (1999), 574-584. MR 1709705 (2000e:35110)

2.
K. Deng and C.-L. Zhao, Blow-up versus quenching, Comm. Appl. Anal. 7 (2003), 87-100. MR 1954906 (2003j:35170)

3.
M. Fila and H.A. Levine, Quenching on the boundary, Nonlinear Anal. TMA 21 (1993), 795-802. MR 1246508 (95b:35028)

4.
A. Friedman and B. Mcleod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447. MR 0783924 (86j:35089)

5.
H.A. Levine, Quenching, nonquenching, and beyond quenching for solutions of some parabolic equations, Ann. Mat. Pura Appl. 155 (1989), 243-260. MR1042837 (91m:35028)

6.
C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. MR 1212084 (94c:35002)

7.
T.I. Zelenyak, Stabilisation of solutions of boundary value problems for a second-order equation with one space variable, Differential Equations 4 (1968), 17-22.

Similar Articles:

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 34B18, 35B05, 35B35, 35K60

Retrieve articles in all Journals with MSC (2000): 34B18, 35B05, 35B35, 35K60

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

PII: S0033-569X-05-00946-2
Received by editor(s): July 24, 2003
Posted: January 19, 2005
Additional Notes: The work of the first author was supported in part by the National Science Foundation under grant DMS-0211412
Copyright of article: Copyright 2005, Brown University


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2008 Brown University
Comments: qam-query@ams.org		 AMS Website