# Blow-up on the boundary: a survey

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 67-78
- ISSN: 0137-6934

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topFila, Marek, and Filo, Ján. "Blow-up on the boundary: a survey." Banach Center Publications 33.1 (1996): 67-78. <http://eudml.org/doc/262535>.

@article{Fila1996,

author = {Fila, Marek, Filo, Ján},

journal = {Banach Center Publications},

keywords = {blow-up; critical Fujita exponent},

language = {eng},

number = {1},

pages = {67-78},

title = {Blow-up on the boundary: a survey},

url = {http://eudml.org/doc/262535},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Fila, Marek

AU - Filo, Ján

TI - Blow-up on the boundary: a survey

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 67

EP - 78

LA - eng

KW - blow-up; critical Fujita exponent

UR - http://eudml.org/doc/262535

ER -

## References

top- [B] F. V. Bunkin, V. A. Galaktionov, N. A. Kirichenko, S. P. Kurdyumov and A. A. Samarskiĭ, Localization in a nonlinear problem of ignition by radiation, Dokl. Akad. Nauk SSSR 302 (1988), 68-71. Zbl0694.35073
- [CY] J. M. Chadam and H. M. Yin, A diffusion equation with localized chemical reactions, Proc. Edinburgh Math. Soc. 37 (1994), 101-118. Zbl0790.35045
- [CFQ] M. Chipot, M. Fila and P. Quittner, Stationary solutions, blowup and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions, Acta Math. Univ. Comen. 60 (1991), 35-103. Zbl0743.35038
- [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. Comenian. 63 (1994), 169-192. Zbl0824.35048
- [Fa] M. Fila, Boundedness of global solutions for the heat equation with nonlinear boundary conditions, Comment. Math. Univ. Carolin. 30 (1989), 479-484. Zbl0702.35141
- [FL] M. Fila and H. A. Levine, Quenching on the boundary, Nonlinear Anal. 21 (1993), 795-802. Zbl0809.35043
- [FQ] 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. Zbl0735.35014
- [Fo1] J. Filo, Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions, Comment. Math. Univ. Carolin. 30 (1989), 485-495. Zbl0702.35142
- [Fo2] J. Filo, Diffusivity versus absorption through the boundary, J. Differential Equations 99 (1992), 281-305. Zbl0761.35048
- [Fo3] J. Filo, Local existence and ${L}^{\infty}$-estimate of weak solutions to a nonlinear degenerate parabolic equation with nonlinear boundary data, Panamerican Math. J. 4 (1994), 1-31. Zbl0849.35061
- [GKS] V. A. Galaktionov, S. P. Kurdyumov and A. A. Samarskiĭ, On the method of stationary states for quasilinear parabolic equations, Math. USSR-Sb. 67 (1990), 449-471. Zbl0701.35010
- [GL] V. A. Galaktionov and H. A. Levine, On critical Fujita exponents for heat equations with a nonlinear flux condition on the boundary, preprint.
- [H1] B. Hu, Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition, Differential Integral Equations 7 (1994), 301-313. Zbl0820.35062
- [H2] B. Hu, Nondegeneracy and single-point-blowup for solution of the heat equation with a nonlinear boundary condition, University of Notre Dame preprint No. 203 (1994).
- [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. Zbl0823.35020
- [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. Differential Equations 16 (1974), 319-334. Zbl0285.35035
- [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. Zbl0293.35004
- [LS] H. A. Levine and R. A. Smith, A potential well theory for the heat equation with a nonlinear boundary condition, Math. Methods Appl. Sci. 9 (1987), 127-136. Zbl0646.35049
- [L] G. Lieberman, Study of global solutions of parabolic equations via a priori estimates. Part I: Equations with principal elliptic part equal to the Laplacian, ibid. 16 (1993), 457-474. Zbl0797.35093
- [LMW1] J. López Gómez, V. Márquez and N. Wolanski, Blow up results and localization of blow up points for the heat equation and localization of blow up points for the heat equation with a nonlinear boundary condition, J. Differential Equations 92 (1991), 384-401. Zbl0735.35016
- [LMW2] J. López Gómez, V. Márquez and N. Wolanski, Global behavior of positive solutions to a semilinear equation with a nonlinear flux condition, IMA Preprint Series No. 810 (1991).
- [Q] P. Quittner, On global existence and stationary solutions for two classes of semilinear parabolic problems, Comment. Math. Univ. Carolin. 34 (1993), 105-124. Zbl0794.35089
- [Wa] 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. Zbl0268.35052
- [WW] M. Wang and Y. Wu, Global existence and blow-up problems for quasilinear parabolic equations with nonlinear boundary conditions, ibid. 24 (1993), 1515-1521. Zbl0790.35042
- [Wo] N. Wolanski, Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary, ibid. 24 (1993), 317-326. Zbl0778.35047
- [Y] H. M. Yin, Blowup versus global solvability for a class of nonlinear parabolic equations, Nonlinear Anal., to appear.

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