Abstract:
We find a bound for the modulus of continuity of the blow-up time for the semilinear parabolic problem ut = Δu + |u|p-1 u, with respect to the initial data.
Registro:
Documento: |
Artículo
|
Título: | On the dependence of the blow-up time with respect to the initial data in a semilinear parabolic problem |
Autor: | Groisman, P.; Rossi, J.D.; Zaag, H. |
Filiación: | Univ. de San Andrés, Victoria, Pcia. de Buenos Aires, Argentina Departamento de Matemática, FCEyN., UBA, Buenos Aires, Argentina CNRS UMR 8553, Dépt. de Math. et Applic., Ecole Normale Supérieure, 45 rue d'Ulm, F-75230 Paris Cedex 05, France
|
Palabras clave: | Blow-up time; Continuity; Parabolic equations |
Año: | 2003
|
Volumen: | 28
|
Número: | 3-4
|
Página de inicio: | 737
|
Página de fin: | 744
|
DOI: |
http://dx.doi.org/10.1081/PDE-120020494 |
Título revista: | Communications in Partial Differential Equations
|
Título revista abreviado: | Commun. Partial Differ. Equ.
|
ISSN: | 03605302
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v28_n3-4_p737_Groisman |
Referencias:
- Ball, J., Remarks on blow-up and nonexistence theorems for nonlinear evolution equations (1977) Quart J Math Oxford, 28, pp. 473-486
- 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
- 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
- Fermanian, K.C., Merle, F., Zaag, H., Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view (2000) Math Ann, 317, pp. 195-237
- Friedman, A., Remarks on nonlinear diffusion equations (1965) Proc. Sympos. Appl. Math. XVII, pp. 2-23. , Amer. Math. Soc.: Providence, R.I
- Friedman, A., Mc Leod, J.B., Blow up of positive solutions of semilinear heat equations (1985) Indiana Univ Math J, 34, pp. 425-447
- Fujita, H., On the blowing up of solutions of the Cauchy problem for ut = Δu + u1+a (1966) J Fac Sci Univ Tokyo Sect IA Math, 13, pp. 109-124
- Galaktionov, V., Vazquez, J.L., Continuation of blow-up solutions of nonlinear heat equations in several space dimensions (1977) Comm Pure Appl Math, 50, pp. 1-67
- Giga, Y., Kohn, R.V., Characterizing blowup using similarity variables (1987) Indiana Univ Math J, 36, pp. 1-40
- Giga, Y., Kohn, R.V., Nondegeneracy of blow up for semilinear heat equations (1989) Comm Pure Appl Math, 42, pp. 845-884
- Giga, Y., Matsui, S., Sasayama, S., (2002) Blow-up Rate for Semilinear Heat Equation with Subcritical Nonlinearity, , preprint
- Herrero, M.A., Velázquez, J.J.L., Flat blow up in one-dimensional, semilinear parabolic problems (1992) Differential Integral Equations, 5 (5), pp. 973-997
- Herrero, M.A., Velázquez, J.J.L., Generic behavior of one-dimensional blow up patterns (1992) Ann Scuola Norm Sup di Pisa, 19 (3), pp. 381-950
- Levine, H.A., Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put = -Au + F(u) (1973) Arch Rational Mech Anal, 51, pp. 371-386
- Merle, F., Solution of a nonlinear heat equation with arbitrarily given blow-up points (1992) Comm Pure Appl Math, 45, pp. 263-300
- Merle, F., Zaag, H., Optimal estimates for blowup rate and behavior for nonlinear heat equations (1998) Comm Pure Appl Math, 51, pp. 139-196
- Merle, F., Zaag, H., Refined uniform estimates at blow-up and applications for nonlinear heat equations (1998) Geom Funct Anal, 8, pp. 1043-1085
- Merle, F., Zaag, H., A Liouville theorem for vector-valued nonlinear heat equations and applications (2000) Math Ann, 316, pp. 103-137
- Pao, C.V., (1992) Nonlinear Parabolic and Elliptic Equations, , New York: Plenum Press
- Quittner, P., Continuity of the blow-up time and a priori bounds for solutions in superlinear parabolic problems Houston J Math, , In press
- Samarskii, A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., (1995) Blow-up in Quasilinear Parabolic Equations, , Berlin: Walter de Gruyter
- Zaag, H., One dimensional behavior of singular N dimensional solutions of semilinear heat equations (2002) Comm Math Phys, 225, pp. 523-549
Citas:
---------- APA ----------
Groisman, P., Rossi, J.D. & Zaag, H.
(2003)
. On the dependence of the blow-up time with respect to the initial data in a semilinear parabolic problem. Communications in Partial Differential Equations, 28(3-4), 737-744.
http://dx.doi.org/10.1081/PDE-120020494---------- CHICAGO ----------
Groisman, P., Rossi, J.D., Zaag, H.
"On the dependence of the blow-up time with respect to the initial data in a semilinear parabolic problem"
. Communications in Partial Differential Equations 28, no. 3-4
(2003) : 737-744.
http://dx.doi.org/10.1081/PDE-120020494---------- MLA ----------
Groisman, P., Rossi, J.D., Zaag, H.
"On the dependence of the blow-up time with respect to the initial data in a semilinear parabolic problem"
. Communications in Partial Differential Equations, vol. 28, no. 3-4, 2003, pp. 737-744.
http://dx.doi.org/10.1081/PDE-120020494---------- VANCOUVER ----------
Groisman, P., Rossi, J.D., Zaag, H. On the dependence of the blow-up time with respect to the initial data in a semilinear parabolic problem. Commun. Partial Differ. Equ. 2003;28(3-4):737-744.
http://dx.doi.org/10.1081/PDE-120020494