@article{AIHPC_1988__5_1_1_0,
author = {Bebernes, J. and Eberly, D.},
title = {A description of self-similar blow-up for dimensions $n \ge 3$},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1--21},
year = {1988},
publisher = {Gauthier-Villars},
volume = {5},
number = {1},
zbl = {0726.35018},
language = {en},
url = {https://www.numdam.org/item/AIHPC_1988__5_1_1_0/}
}
TY - JOUR AU - Bebernes, J. AU - Eberly, D. TI - A description of self-similar blow-up for dimensions $n \ge 3$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 1988 SP - 1 EP - 21 VL - 5 IS - 1 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPC_1988__5_1_1_0/ LA - en ID - AIHPC_1988__5_1_1_0 ER -
Bebernes, J.; Eberly, D. A description of self-similar blow-up for dimensions $n \ge 3$. Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 1, pp. 1-21. https://www.numdam.org/item/AIHPC_1988__5_1_1_0/
[1] , and , A Description of Blow-Up for the Solid Fuel Ignition Model, Indiana Univ. Math. J., Vol. 36, 1987, pp. 295-305. | MR
[2] and , A Mathematical Analysis of Blow-up for Thermal Reactions, S.I.A.M. J. Appl. Math., Vol. 40, 1981, pp. 476-484. | Zbl | MR
[3] and , On the Existence of Solutions to the Kassoy Problem in Dimension 1, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 1157-1162. | Zbl | MR
[4] , A Criterion for Blow-Up of Solutions to Semilinear Heat Equations, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 722-727. | Zbl | MR
[5] , On the Existence of Solutions to the Kassoy Problem on Dimensions 1 and 2, J. Math. Anal. Appl. (to appear). | MR
[6] and , On the Existence of Logarithmic-Type Solutions to the Kassoy Problem in Dimension 3, J. Differential Equations (to appear). | MR
[7] and , Blow-Up of Positive Solutions of Seminlinear Heat Equations, Indiana Univ. Math. J., Vol. 34, No. 2, 1985, pp. 425-447. | Zbl | MR
[8] and , Asymptotically Self-Similar Blow-Up of Semilinear Heat Equations, Comm. Pure and Appl. Math., Vol. 38, 1985, pp. 297-319. | Zbl | MR
[9] , Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions, S.I.A.M. J. Appl. Math., Vol. 43, 1983, pp. 1350-1366. | Zbl | MR
[10] , The Existence of Bounded Solutions for a Semilinear Heat Equation, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 332-336. | Zbl | MR
[11] and , Characterizing Blowup Using Similarity Variables, Indiana Univ. Math. J., Vol. 36, 1987, pp. 1-40. | Zbl | MR
[12] and , The Equation ut=uxx+uβ. Localization and Asymptotic Behavior of Unbounded Solutions, Diff. Uravnen, Vol. 22, 1986, pp. 1165-1173.
[13] , On Elliptic Equations Related to Self-Similar Solutions for Nonlinear Heat Equations, Hiroshima Math. J., Vol. 16, 1986, pp. 541-554. | Zbl | MR
[14] , and , A Nonlinear Instability Burst in Plane Parallel Flow, J. Fluid Mech., Vol. 51, 1972, pp. 705-735. | Zbl
[15] , Reactive-Diffusive Systems with Arrhenius Kinetics: Dynamics of Ignition, S.I.A.M. J. Appl. Math., Vol. 39, 1980, pp. 21-36. | Zbl | MR
[16] and , The Thermal Explosion Confined by a Constant Temperature Boundary: I. The Induction Period Solution, S.I.A.M. J. Appl. Math., Vol. 39, 1980, pp. 412-430. | Zbl | MR
[17] , Single Point Blowup of Semilinear Initial Value Problems, J. Diff. Eq., Vol. 55, 1984, pp. 204-224. | Zbl | MR
[18] , An L∞ Blowup Estimate for a Nonlinear Heat Equation, Comm. Pure Appl. Math., Vol. 38, 1985, pp. 291-296. | Zbl | MR






