The blow-up for weakly coupled reaction-diffusion systems

Author:
Liwen Wang

Journal:
Proc. Amer. Math. Soc. **129** (2001), 89-95

MSC (2000):
Primary 35K55, 35K57, 35K40

DOI:
https://doi.org/10.1090/S0002-9939-00-05860-3

Published electronically:
August 17, 2000

MathSciNet review:
1784017

Full-text PDF

Abstract | References | Similar Articles | Additional Information

In this paper we consider a weakly coupled parabolic system with nonnegative exponents in the forcing functions. We find the conditions which result in blow-up in finite time. Also, we obtain the blow-up rate.

**1.**Deng, K., Blow-up rates for parabolic systems, Z. Angew Math. Phys., 46, 110-118 (1995).**2.**Escobedo, M. and Herrero, M. A., Boundedness and blowup for a semilinear reaction-diffusion system, J. Diff. Equ., 89, 176-202 (1991).**3.**Escobedo, M. and Levine, H.A., Critical blowup and global existence numbers for a weakly coupled system of reaction-differential equations, Arch. Rational Mech. Anal. 129, 47-100 (1995). MR**96d:35063****4.**Friedman, A. and Giga, Y., A single point blow-up for solutions of semilinear parabolic systems, J. Fac. Sci. Univ. Tokyo Sec. IA Math. 34, 65-79 (1987). MR**89b:35066****5.**Friedman, A and Mcleod, B., Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34, 425-447 (1985). MR**86j:35089****6.**Galaktionov, V. A., Kurdyumov, S. P., and Samarskii, A. A., A parabolic system of quasilinear equations, I Differential Equations 21, 1049-1062 (1985).**7.**Galaktionov, V. A., Kurdyumov, S. P., and Samarskii, A. A., A parabolic system of quasilinear equations. II Differential Equations 19, 1558-1571 (1983).**8.**Hu, B. and Yin, H.-M., The profile near blowup time for the solution of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346, 117-135 (1995). MR**95c:35040****9.**Pao,*C.-V., Nonlinear Parabolic and Elliptic Equations*, Plenum Press, New York 1992.**10.**Rossi J., The blow-up rate for a system of heat equation with non-trivial coupling at the boundary, Math. Meth. Appl. Sci. 20, 1-11 (1997). MR**97k:35099****11.**Samarskii, A. A., Galaktionov, V. A., Kurdyumov, S. P., and Mikhailov, A. P.,*Blow-up in Quasilinear Parabolic Equations*, Walter de Gruyter, Berlin, 1995. MR**96b:35003****12.**Wang L., The blow-up for a semilinear parabolic system. Mathematica Applicata (complement), 104-106 (1995).**13.**Zhang, K., On the blow-up rate of solution of semilinear parabolic equations system, J. Math. Study 27, No. 2, 102-108(1994).**14.**Zhang, K., Blow-up phenomena in solutions of systems of semilinear parabolic equations, J. Math. Res. Exposition 15, No. 1, 83-90(1995). MR**96b:35102**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
35K55,
35K57,
35K40

Retrieve articles in all journals with MSC (2000): 35K55, 35K57, 35K40

Additional Information

**Liwen Wang**

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

Address at time of publication:
Department of Computer Science, University of Louisiana at Lafayette, Lafayette, Louisiana 70504

Email:
lxw0340@usl.edu, lxw0340@usl.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05860-3

Keywords:
Blow-up,
weakly coupled reaction-diffusion system

Received by editor(s):
March 7, 1999

Published electronically:
August 17, 2000

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2000
American Mathematical Society