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A quenching criterion for a multi-dimensional parabolic problem due to a concentrated nonlinear source. (English) Zbl 1225.35121
Summary: A multi-dimensional parabolic first initial-boundary value problem with a concentrated nonlinear source is studied. A criterion for its solution to quench, in a finite time t q , everywhere on the concentrated nonlinear source only is given. An upper bound for t q is also deduced. For illustration, an example is given.
MSC:
35K58Semilinear parabolic equations
35K20Second order parabolic equations, initial boundary value problems
35B35Stability of solutions of PDE
References:
[1]Chan, C. Y.; Kong, P. C.: A thermal explosion model, Appl. math. Comput. 71, 201-210 (1995) · Zbl 0832.35141 · doi:10.1016/0096-3003(94)00154-V
[2]Chan, C. Y.: Quenching criteria for a degenerate parabolic problem due to a concentrated nonlinear source, Dynam. systems appl. 18, 121-127 (2009) · Zbl 1172.35434
[3]Chan, C. Y.; Tian, H. Y.: Single-point blow-up for a degenerate parabolic problem due to a concentrated nonlinear source, Quart. appl. Math. 61, 363-385 (2003) · Zbl 1032.35105
[4]Chan, C. Y.: Multi-dimensional quenching due to a concentrated nonlinear source, , 273-278 (2006)
[5]Chan, C. Y.; Tragoonsirisak, P.: A multi-dimensional quenching problem due to a concentrated nonlinear source in RN, Nonlinear anal. 69, 1494-1514 (2008) · Zbl 1176.35011 · doi:10.1016/j.na.2007.07.001
[6]Mcowen, R. C.: Partial differential equations: methods and applications, (2003)
[7]Friedman, A.: Partial differential equations of parabolic type, (1964) · Zbl 0144.34903
[8]Haberman, R.: Applied partial differential equations with Fourier series and boundary value problems, (2004)
[9]Kawarada, H.: On solutions of initial-boundary problem for ut=uxx+1/(1-u), Publ. res. Inst. math. Sci. 10, 729-736 (1975) · Zbl 0306.35059 · doi:10.2977/prims/1195191889