Numerical quenching for the semilinear heat equation with a singular absorption

Journal of Computational and Applied Mathematics

Volumn 228, Issue 1, 2009, Pages 92-103

  Ferreira, Raúl ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Numerical quenching; Semilinear heat equation; Singular absorption

Indexed keywords

HEAT TRANSFER; PARTIAL DIFFERENTIAL EQUATIONS;

HEAT EQUATION; NUMERICAL APPROXIMATIONS; NUMERICAL RESULTS; QUENCHING RATE; QUENCHING TIME; SEMILINEAR HEAT EQUATION;

QUENCHING;

EID: 63549107315     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.08.041     Document Type: Article

References (12)

1. Friedman A. Partial Differential Equation of Parabolic Type (1969), Prentice-Hall, Englewood Cliffs
2. Levine H.A. Quenching and beyond: A survey of recent results. Nonlinear Mathematical Problems in Industry II. GAKUTO Internat. Ser. Math. Sci. Appl. vol. 2 (1993), Gakkōtosho, Tokyo 501-512
3. x x + 1 / (1 - u). Publ. Res. Inst. Math. Sci. 10 (1974/75) 729-736
4. Chan C.Y. Recent advances in quenching phenomena. Proc. Dynam. Systems. Appl. 2 (1996) 107-113
5. Fila M., and Levine H.A. Quenching on the boundary. Nonlinear Anal. 21 (1993) 795-802
6. Levine H.A. The phenomenon of quenching: A survey. In: Lakshmikantham V. (Ed). Trends in the Theory and Practice of Nonlinear Analysis (1985), Elsevier Science Publ., North Holland 275-286
7. Liang K.W., Lin P., and Tan R.C.E. Numerical solution of quenching problems using mesh-dependent variable temporal steps. Appl. Numer. Math. 57 (2007) 791-800
8. Sheng Q., and Cheng H. An adaptive grid method for degenerate semilinear quenching problems. Comput. Math. Appl. 39 (2000) 57-71
9. Sheng Q., and Khaliq A.Q.M. A compound adaptive approach to degenerate nonlinear quenching problems. Numer. Methods Partial Differential Equations 15 (1999) 29-47
10. Guo J.S. On the quenching behaviour of the solution of a semilinear parabolic equation. J. Math. Anal. Appl. 151 (1990) 58-79
11. Guo J.S. On the quenching rate estimate. Quart. Appl. Math. 49 (1991) 747-752
12. Groisman P. Totally discrete explicit and semi-implicit Euler methods for a blow-up problem in several space dimensions. Computing 76 (2006) 325-352