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## Banach Center Publications

2000 | 52 | 1 | 61-71
Tytuł artykułu

### Some recent results on blow-up on the boundary for the heat equation

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
61-71
Opis fizyczny
Daty
wydano
2000
Twórcy
autor
• Institute of Applied Mathematics, Faculty of Mathematics and Physics, Comenius University, 842 15 Bratislava, Slovakia
autor
• Institute of Applied Mathematics, Faculty of Mathematics and Physics, Comenius University, 842 15 Bratislava, Slovakia
Bibliografia
• [A] H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differ. Equations 72 (1988), 201-269.
• [C] M. Chlebík, Asymptotics of blowup for the heat equation with a nonlinear boundary condition, preprint.
• [CF1] M. Chlebík and M. Fila, From critical exponents to blow-up rates for parabolic problems, Rend. Mat. Appl., to appear.
• [CF2] M. Chlebík and M. Fila, On the blow-up rate for the heat equation with a nonlinear boundary condition, preprint.
• [D] K. Deng, Blow-up rates for parabolic systems, Z. angew. Math. Phys. 47 (1996), 132-143.
• [DFL] K. Deng, M. Fila and H. A. Levine, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenianae 63 (1994), 169-192.
• [Fa] M. Fila, Boundedness of global solutions for the heat equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinae 30 (1989), 479-484.
• [FF] M. Fila and J. Filo, Blow-up on the boundary: A survey, in: S. Janeczko et al. (eds.), Singularities and Differential Equations, Banach Center Publ. 33, Polish Academy of Sciences, Warsaw (1996), 67-78.
• [FFL] M. Fila, J. Filo and G. M. Lieberman, Blow-up on the boundary for the heat equation, Calc. Var. 10 (2000), 85-99.
• [FQ1] M. Fila and P. Quittner, The blowup rate for the heat equation with a nonlinear boundary condition, Math. Methods Appl. Sci. 14 (1991), 197-205.
• [FQ2] M. Fila and P. Quittner, Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition, in: Topics in Nonlinear Analysis, The Herbert Amann Volume, Birkhäuser Verlag (1998), 252-272.
• [Fo] J. Filo, Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinae 30 (1989), 485-495.
• [H1] B. Hu, Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition, Diff. Int. Equations 7 (1994), 301-313.
• [H2] B. Hu, Nondegeneracy and single-point-blowup for solution of the heat equation with a nonlinear boundary condition, J. Math. Sci. Univ. Tokyo 1 (1995), 251-276.
• [H3] B. Hu, Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition, Differ. Int. Equations 9 (1996), 891-901.
• [HY] B. Hu and H.-M. Yin, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc. 346 (1994), 117-135.
• [L] H. A. Levine, Some nonexistence and instability theorems for solutions of formally parabolic equations of the form $Pu_t=-Au+F(u)$, Arch. Rat. Mech. Anal. 51 (1973), 371-386.
• [LP1] H. A. Levine and L. E. Payne, Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time, J. Diff. Equations 16 (1974), 319-334.
• [LP2] H. A. Levine and L. E. Payne, Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints, Proc. Amer. Math. Soc. 46 (1974), 277-284.
• [LX] Z. Lin and C. Xie, The blow-up rate for a system of heat equations with nonlinear boundary conditions, Nonlin. Anal. TMA 34 (1998), 767-778.
• [Q] P. Quittner, Global existence of solutions of parabolic problems with nonlinear boundary conditions, in: S. Janeczko et al. (eds.), Singularities and Differential Equations, Banach Center Publ. 33, Polish Academy of Sciences, Warsaw (1996), 309-314.
• [R] J. D. Rossi, The blow-up rate for a system of heat equations with non-trivial coupling at the boundary, Math. Methods Appl. Sci. 20 (1997), 1-11.
• [W] W. Walter, On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition, SIAM J. Math. Anal. 6 (1975), 85-90.
• [WXW] S. Wang, C. Xie and M. Wang, Note on critical exponents for a system of heat equations coupled in the boundary conditions, J. Math. Anal. Appl. 218 (1998), 313-324.
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Bibliografia
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