Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions

Discrete and Continuous Dynamical Systems - Series B

Volumn 2, Issue 2, 2002, Pages 279-294

  Acosta, G ^a,b   Bonder, J Fernández ^a   Groisman, P ^a   Rossi, J D ^a  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b Universidad ae Buenos Aires   (Argentina)

Author keywords

Asymptotic; Blow up; Parabolic equations; Semidiscretization in space

Indexed keywords

EID: 0042261532     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2002.2.279     Document Type: Article

References (22)

1. L. M. Abia, J. C. Lopez-Marcos, J. Martinez. BLOW-UP FOR SEMIDISCRETIZATIONS OF REACTION DIFFUSION EQUATIONS. Appl. Numer. Math. Vol 20, (1996), 145-156.
2. L. M. Abia, J. C. Lopez-Marcos, J. Martinez. ON THE BLOW-UP TIME CONVERGENCE OF SEMIDISCRETIZATIONS OF REACTION DIFFUSION EQUATIONS. Appl. Numer. Math. Vol 26, (1998), 399-414.
3. C. Bandle and H. Brunner. BLOW-UP IN DIFFUSION EQUATIONS: A SURVEY. J. Comp. Appl. Math. Vol. 97, (1998), 3-22.
4. M. Berger and R. V. Kohn. A RESCALING ALGORITHM FOR THE NUMERICAL CALCULATION OF BLOWING UP SOLUTIONS. Comm. Pure Appl. Math. Vol 41, (1988), 841-863.
5. C. J. Budd, W. Huang and R. D. Russell. MOVING MESH METHODS FOR PROBLEMS WITH BLOW-UP. SIAM Jour. Sci. Comput. Vol 17(2), (1996), 305-327.
6. P. Ciarlet. The finite element method for elliptic problems. North Holland, (1978).
7. P. Ciarlet and P.A. Raviart. MAXIMUM PRICIPLE AND UNIFORM CONVERGENCE FOR THE FINITE ELEMENT METHOD. Comput. Methods Appl. Mech. Engrg. Vol. 2 (1973), 17-31.
8. R. G. Duran, J. I. Etcheverry and J. D. Rossi. NUMERICAL APPROXIMATION OF A PARABOLIC PROBLEM WITH A NONLINEAR BOUNDARY CONDITION. Discr. and Cont. Dyn. Sys. Vol. 4 (3), (1998), 497-508.
9. Y. Giga and R. V. Kohn. NONDEGENERACY OF BLOW UP FOR SEMILINEAR HEAT EQUATIONS. Comm. Pure Appl. Math. Vol. 42, (1989), 845-884.
10. P. Groisman and J.D. Rossi. ASYMPTOTIC BEHAVIOUR OF A NUMERICAL APPROXIMATION FOR A PARABOLIC PROBLEM WITH BLOWING-UP SOLUTIONS, J. Comput. Appl. Math. Vol. 135, (2001), 135-155.
11. F. Harary. Graph Theory. Addison-Wesley. 1969.
12. D. Henry. Geometric theory of semilinear parabolic equation. Lecture Notes in Math, vol 840. Springer Verlag. 1981.
13. B. Hu. NONDEGENERACY AND SINGLE-POINT-BLOWUP FOR SOLUTION OF THE HEAT EQUATION WITH AS NONLINEAR BOUNDARY CONDITION, J. Math. Sci. Univ. Tokyo, V. 1, 1994, 251-276.
14. B. Hu and H.M. Yin. THE PROFILE NEAR BLOW-UP TIME FOR THE SOLUTION OF THE HEAT EQUATION WITH A NONLINEAR BOUNDARY CONDITION, Trans. Amer. Math. Soc., 346(1)(1995), 117-135.
15. M. A. Herrero and J. J. L. Velazquez. FLAT BLOW UP IN ONE-DIMENSIONAL, SEMILINEAR PARABOLIC PROBLEMS, Differential Integral Equations. Vol. 5(5), (1992), 973-997.
16. M. A. Herrero and J. J. L. Velazquez. GENERIC BEHAVIOUR OF ONE-DIMENSIONAL BLOW UP PATTERNS. Ann. Scuola Norm. Sup. di Pisa, Vol. XIX (3), (1992), 381-950.
17. K.W. Morton and D.F. Mayers. Numerical Solution of partial differential equations. Cambridge University Press, Cambridge (1994).
18. T. Nakagawa and T. Ushijima. FINITE ELEMENT ANALYSIS OF THE SEMI-LINEAR HEAT EQUATION OF BLOW-UP TYPE. Topics in numerical analysis III, Proc. R. Irish Acad. Conf., Dublin 1976, (1977), 275-291.
19. C.V. Pao. Nonlinear parabolic and elliptic equations. Plenum Press 1992.
20. D.F. Rial and J.D. Rossi. BLOW-UP RESULTS AND LOCALIZATION OF BLOW-UP POINTS IN AN N-DIMENSIONAL SMOOTH DOMAIN, Duke Math. Jour. 88 (2) (1997), 391-405.
21. A. Samarski, V. A. Galacktionov, S. P. Kurdyunov and A. P. Mikailov. Blow-up in quasilinear parabolic equations. Walter de Gruyter, Berlin, (1995).
22. W. Walter. ON EXISTENCE AND NONEXISTENCE IN THE LARGE OF SOLUTIONS OF PARABOLIC DIFFERENTIAL EQUATIONS WITH A NONLINEAR BOUNDARY CONDITION, SIAM J. Math. Anal., 6(1) (1975), 85-90.