@article{AIHPC_1996__13_6_707_0, author = {Hu, Bei and Yin, Hong-Ming}, title = {On critical exponents for the heat equation with a nonlinear boundary condition}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {707--732}, publisher = {Gauthier-Villars}, volume = {13}, number = {6}, year = {1996}, mrnumber = {1420495}, zbl = {0908.35066}, language = {en}, url = {http://archive.numdam.org/item/AIHPC_1996__13_6_707_0/} }
TY - JOUR AU - Hu, Bei AU - Yin, Hong-Ming TI - On critical exponents for the heat equation with a nonlinear boundary condition JO - Annales de l'I.H.P. Analyse non linéaire PY - 1996 SP - 707 EP - 732 VL - 13 IS - 6 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_1996__13_6_707_0/ LA - en ID - AIHPC_1996__13_6_707_0 ER -
%0 Journal Article %A Hu, Bei %A Yin, Hong-Ming %T On critical exponents for the heat equation with a nonlinear boundary condition %J Annales de l'I.H.P. Analyse non linéaire %D 1996 %P 707-732 %V 13 %N 6 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPC_1996__13_6_707_0/ %G en %F AIHPC_1996__13_6_707_0
Hu, Bei; Yin, Hong-Ming. On critical exponents for the heat equation with a nonlinear boundary condition. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 6, pp. 707-732. http://archive.numdam.org/item/AIHPC_1996__13_6_707_0/
[1] On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains, Trans. Amer. Math. Soc., Vol. 316, 1989, pp. 595-624. | MR | Zbl
and ,[2] On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenianae, Vol. 63, 1994, pp. 169-192. | MR | Zbl
, and ,[3] Boundedness of global solutions for the heat equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinate, Vol. 30, 1989, pp. 479-484. | MR | Zbl
,[4] Blow-up on the boundary: a survey, Proceedings of the Banach Center, to appear. | MR | Zbl
and ,[5] On the blowing up of solutions of the Cauchy problem for ut = Δu + u1+α, J. Fac. Sci. Univ. Tokyo Sect. A. Math., Vol. 16, 1966, pp. 105-113.
,[6] On critical Fujita exponents for heat equations with a nonlinear flux boundary condition on the boundary, Israel J. Math., to appear. | Zbl
and ,[7] Green functions for second order parabolic integrodifferential problems, Longman Scientific and Technical, New York, 1992. | MR | Zbl
and ,[8] Blow up and localization of blow up points for the heat equation with a nonlinear boundary condition, J. Diff. Eq., Vol. 2, 1992, pp. 384-401. | MR | Zbl
, and ,[9] Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition, Differential and Integral Equations, Vol. 7, 1994, pp. 301-313. | MR | Zbl
,[10] The profile near blow up time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., Vol. 346, 1994, pp. 117-135. | MR | Zbl
and ,[11] Linear and Quasilinear Equations of Parabolic type, AMS Monograph translation, Vol. 23, Providence, RI, 1968. | MR | Zbl
, and ,[12] The role of critical exponents in blow up theorems, SIAM Review, Vol. 32, 1990, pp. 262-288. | MR | Zbl
,[13] The value of the critical exponent for reaction-diffusion equations in cones, Arch. Rational Mech. Anal., Vol. 109, 1990, pp. 73-80. | MR | Zbl
and ,[14] Study of global solutions of parabolic equations via a priori estimates, Part I: Equations with principal elliptic part equal to the Laplacian, Math. Meth. in the Appl. Sci., Vol. 16, 1993, pp. 457-474. | MR | Zbl
,[15] Sobolev Spaces, Springer-Verlag, New York, 1985.
,[16] Critical exponent of blow up for semilinear heat equation on a product domain, J. Fac. Sci. Univ. Tokyo, Sect. IA, Math., Vol. 40, 1993, pp. 635-650. | MR | Zbl
and ,[17] Nonlinear Parabolic Equation and Elliptic Equations, Plenum Press, New York, 1992. | Zbl
,[18] On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition, SIAM J. Math. Anal., Vol. 6, 1975, pp. 85-90. | MR | Zbl
,[19] Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math., Vol. 38, 1981, pp. 29-40. | MR | Zbl
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