A description of self-similar blow-up for dimensions n3
Annales de l'I.H.P. Analyse non linéaire, Volume 5 (1988) no. 1, p. 1-21
@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},
     publisher = {Gauthier-Villars},
     volume = {5},
     number = {1},
     year = {1988},
     pages = {1-21},
     zbl = {0726.35018},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1988__5_1_1_0}
}
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, Volume 5 (1988) no. 1, pp. 1-21. http://www.numdam.org/item/AIHPC_1988__5_1_1_0/

[1] J. Bebernes, A. Bressan and D. Eberly, A Description of Blow-Up for the Solid Fuel Ignition Model, Indiana Univ. Math. J., Vol. 36, 1987, pp. 295-305. | MR 891776

[2] J. Bebernes and D. Kassoy, A Mathematical Analysis of Blow-up for Thermal Reactions, S.I.A.M. J. Appl. Math., Vol. 40, 1981, pp. 476-484. | MR 614744 | Zbl 0481.35048

[3] J. Bebernes and W. Troy, 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. | MR 892494 | Zbl 0645.34008

[4] H. Bellout, A Criterion for Blow-Up of Solutions to Semilinear Heat Equations, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 722-727. | MR 883564 | Zbl 0645.35041

[5] D. Eberly, On the Existence of Solutions to the Kassoy Problem on Dimensions 1 and 2, J. Math. Anal. Appl. (to appear). | MR 924299

[6] D. Eberly and W. Troy, On the Existence of Logarithmic-Type Solutions to the Kassoy Problem in Dimension 3, J. Differential Equations (to appear). | MR 915490

[7] A. Friedman and B. Mcleod, Blow-Up of Positive Solutions of Seminlinear Heat Equations, Indiana Univ. Math. J., Vol. 34, No. 2, 1985, pp. 425-447. | MR 783924 | Zbl 0576.35068

[8] Y. Giga and R.V. Kohn, Asymptotically Self-Similar Blow-Up of Semilinear Heat Equations, Comm. Pure and Appl. Math., Vol. 38, 1985, pp. 297-319. | MR 784476 | Zbl 0585.35051

[9] A. Lacey, Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions, S.I.A.M. J. Appl. Math., Vol. 43, 1983, pp. 1350-1366. | MR 722946 | Zbl 0543.35047

[10] W. Troy, The Existence of Bounded Solutions for a Semilinear Heat Equation, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 332-336. | MR 876275 | Zbl 0655.35039

[11] Y. Giga and R.V. Kohn, Characterizing Blowup Using Similarity Variables, Indiana Univ. Math. J., Vol. 36, 1987, pp. 1-40. | MR 876989 | Zbl 0601.35052

[12] V.A. Galaktionov and S.A. Posashkov, The Equation ut=uxx+uβ. Localization and Asymptotic Behavior of Unbounded Solutions, Diff. Uravnen, Vol. 22, 1986, pp. 1165-1173.

[13] Y. Giga, On Elliptic Equations Related to Self-Similar Solutions for Nonlinear Heat Equations, Hiroshima Math. J., Vol. 16, 1986, pp. 541-554. | MR 867579 | Zbl 0626.35033

[14] L.M. Hocking, K. Stewartson and J.T. Stuart, A Nonlinear Instability Burst in Plane Parallel Flow, J. Fluid Mech., Vol. 51, 1972, pp. 705-735. | Zbl 0232.76053

[15] A. Kapila, Reactive-Diffusive Systems with Arrhenius Kinetics: Dynamics of Ignition, S.I.A.M. J. Appl. Math., Vol. 39, 1980, pp. 21-36. | MR 585826 | Zbl 0489.76098

[16] D. Kassoy and J. Poland, 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. | MR 593679 | Zbl 0472.76070

[17] F.B. Weissler, Single Point Blowup of Semilinear Initial Value Problems, J. Diff. Eq., Vol. 55, 1984, pp. 204-224. | MR 764124 | Zbl 0555.35061

[18] F.B. Weissler, An L∞ Blowup Estimate for a Nonlinear Heat Equation, Comm. Pure Appl. Math., Vol. 38, 1985, pp. 291-296. | MR 784475 | Zbl 0592.35071