Artículo
Groisman, P.; Rossi, J.D. "Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem" (2004) Asymptotic Analysis. 37(1):79-91
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Abstract:
We find a bound for the modulus of continuity of the blow-up time for the problem ut = λΔu + up, with initial datum u(x, 0) = φ(x) + hf(x) respect to the parameters λ, p and h. We also find an estimate for the rate of convergence of the blow-up times for a semi-discrete numerical scheme.
Registro:
| Documento: | Artículo |
| Título: | Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem |
| Autor: | Groisman, P.; Rossi, J.D. |
| Filiación: | Instituto de Calculo, FCEyN, UBA (1428), Pab. II, Ciudad Universitaria, Buenos Aires, Argentina Departamento de Matemática, FCEyN, UBA (1428), Buenos Aires, Argentina Departamento de Matemática, Universidad Católica de Chile, Casilla 306, Santiago, Chile |
| Palabras clave: | Blow-up; Semidiscretization in space; Semilinear parabolic equations; Approximation theory; Boundary conditions; Convergence of numerical methods; Integral equations; Matrix algebra; Ordinary differential equations; Perturbation techniques; Theorem proving; Blow-up time; Semidiscretization in space; Semilinear parabolic equations; Partial differential equations |
| Año: | 2004 |
| Volumen: | 37 |
| Número: | 1 |
| Página de inicio: | 79 |
| Página de fin: | 91 |
| Título revista: | Asymptotic Analysis |
| Título revista abreviado: | Asymptotic Anal |
| ISSN: | 09217134 |
| CODEN: | ASANE |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v37_n1_p79_Groisman |
Referencias:
- Abia, L.M., Lopez-Marcos, J.C., Martinez, J., Blow-up for semidiscretizations of reaction diffusion equations (1996) Appl. Numer. Math., 20, pp. 145-156
- Abia, L.M., Lopez-Marcos, J.C., Martinez, J., On the blow-up time convergence of semidiscretizations of reaction diffusion equations (1998) Appl. Numer. Math., 26, pp. 399-414
- Ball, J., Remarks on blow-up and nonexistence theorems for nonlinear evolution equations (1977) Quart. J. Math. Oxford, 28, pp. 473-486
- Bandle, C., Brunner, H., Blow-up in diffusion equations: A survey (1998) J. Comput. Appl. Math., 97, pp. 3-22
- Bandle, C., Brunner, H., Numerical analysis of semilinear parabolic problems with blow-up solutions (1994) Rev. Real Acad. Cienc. Exact. Fis. Natur. Madrid, 88, pp. 203-222
- Baras, P., Cohen, L., Complete blow-up after Tmax for the solution of a semilinear heat equation (1987) J. Funct. Anal., 71, pp. 142-174
- Berger, M., Kohn, R.V., A rescaling algorithm for the numerical calculation of blowing up solutions (1988) Comm. Pure Appl. Math., 41, pp. 841-863
- Budd, C.J., Huang, W., Russell, R.D., Moving mesh methods for problems with blow-up (1996) SIAM J. Sci. Comput., 17 (2), pp. 305-327
- Chen, X.Y., Asymptotic behaviours of blowing up solutions for finite difference analogue of ut = uxx + u1+α (1986) J. Fac. Sci. Univ. Tokyo Sect. IA Math., 33, pp. 541-574
- Ciarlet, P., (1978) The Finite Element Method for Elliptic Problems, , North-Holland, Amsterdam
- Chen, X.Y., Matano, H., Convergence, asymptotic periodicity and finite point blow up in one-dimensional semilinear heat equations (1989) J. Differential Equations, 78, pp. 160-190
- Cortázar, C., Del Pino, M., Elgueta, M., The problem of uniqueness of the limit in a semilinear heat equation (1999) Comm. Partial Differential Equations, 24 (11-12), pp. 2147-2172
- Duran, R.G., Etcheverry, J.I., Rossi, J.D., Numerical approximation of a parabolic problem with a nonlinear boundary condition (1998) Discrete Cont. Dyn. Systems, 4 (3), pp. 497-506
- Fermanian Kammerer, C., Zaag, H., Boundedness up to blow-up of the difference between two solutions to a semilinear heat equation (2000) Nonlinearity, 13, pp. 1189-1216
- Friedman, A., Mc Leod, J.C., Blow up of positive solutions of semilinear heat equations (1985) Indiana Univ. Math. J., 34, pp. 425-447
- Galacktionov, V., Vazquez, J.L., Continuation of blow-up solutions of nonlinear heat equations in several space dimensions (1997) Comm. Pure Appl. Math., 50, pp. 1-67
- Giga, Y., Kohn, R.V., Nondegeneracy of blow up for semilinear heat equations (1989) Comm. Pure Appl. Math., 42, pp. 845-884
- Giga, Y., Kohn, R.V., Characterizing blow-up using similarity variables (1987) Indiana Univ. Math. J., 42, pp. 1-40
- Groisman, P., Quirós, F., Rossi, J.D., Non-simultaneous blow-up in numerical approximation of a parabolic system (2002) Comput. Appl. Math., 21 (3), pp. 813-831
- Groisman, P., Rossi, J.D., Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions (2001) J. Comput. Appl. Math., 135, pp. 135-155
- Herrero, M.A., Velazquez, J.J.L., Flat blow up in one-dimensional, semilinear parabolic problems (1992) Differential Integral Equations, 5 (5), pp. 973-997
- Herrero, M.A., Velazquez, J.J.L., Generic behaviour of one-dimensional blow up patterns (1992) Ann. Scuola Norm. Sup. Pisa, 19 (3), pp. 381-950
- Le Roux, M.N., Semidiscretizations in time of nonlinear parabolic equations with blow-up of the solutions (1994) SIAM J. Numer. Anal., 31, pp. 170-195
- Matos, J., Souplet, P., Universal blow-up rates for a semilinear heat equation and applications (2003) Adv. Differential Equations, 8 (5), pp. 615-639
- Merle, F., Solution of a nonlinear heat equation with arbitrarily given blow-up points (1992) Comm. Pure Appl. Math., 45, pp. 263-300
- Pao, C.V., Nonlinear parabolic and elliptic equations (1992), Plenum Press; Quittner, P., Continuity of the blow-up time and a priori bounds for solutions in superlinear parabolic problems (2003) Houston J. Math., 29 (3), pp. 757-799
- Samarski, A., Galacktionov, V.A., Kurdyunov, S.P., Mikailov, A.P., (1995) Blow-up in Quasilinear Parabolic Equations, , Walter de Gruyter, Berlin
- Zaag, H., One dimensional behavior of singular N-dimensional solutions of semilinear heat equations (2002) Comm. Math. Phys., 225 (3), pp. 523-549
Citas:
---------- APA ----------
Groisman, P. & Rossi, J.D. (2004) . Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem. Asymptotic Analysis, 37(1), 79-91.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v37_n1_p79_Groisman [ ]
---------- CHICAGO ----------
Groisman, P., Rossi, J.D. "Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem" . Asymptotic Analysis 37, no. 1 (2004) : 79-91.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v37_n1_p79_Groisman [ ]
---------- MLA ----------
Groisman, P., Rossi, J.D. "Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem" . Asymptotic Analysis, vol. 37, no. 1, 2004, pp. 79-91.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v37_n1_p79_Groisman [ ]
---------- VANCOUVER ----------
Groisman, P., Rossi, J.D. Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem. Asymptotic Anal. 2004;37(1):79-91.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v37_n1_p79_Groisman [ ]
