Blow-up for two nonlinear problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 41, Issue 7, 2000, Pages 825-854

  Ramiandrisoa, Arthur ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; INTEGRODIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SET THEORY; THEOREM PROVING;

BLOW-UP SETS;

NONLINEAR EQUATIONS;

EID: 0034277381     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00312-5     Document Type: Article

References (17)

1. max for the solution of a semilinear heat equation, J. Funct. Anal. 71 (1987) 142-174.
2. P. Baras, M. Pierre, Critère d'existence de solutions positives pour des équations semi-linéaires non monotones, Ann. Inst. Henri Poincaré 2(3) (1985) 185-212.
3. t - ∇u = g(u) revisited, Adv. Differential Equations 1 (1996) 73-90.
4. H. Brezis, T. Cazenave, Nonlinear Evolution Equations, Part 1, to appear.
5. H. Brezis, J.L. Vazquez, Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Complutense Madrid 10 (1997) 443-469.
6. Y.G. Chen, Blow-up solutions of a semilinear parabolic equation with the Neumann and Robin boundary conditions, J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 37 (1990) 537-574.
7. X.Y. Chen, H. Matano, Convergence, asymptotic periodicity and finite point blow-up in one-dimensional semilinear heat equation, J. Differential Equations 78 (1989) 160-190.
8. M.G. Crandall, P.H. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Rat. Mech. Anal. 58 (1975) 207-218.
9. A. Friedman, B. McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34(2) (1985) 425-447.
10. D.D. Joseph, T.S. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal. 49 (1973) 241-269.
11. H.B. Keller, J. Keener, Positive solutions of convex nonlinear eigenvalue problems, J. Differential Equations 16 (1974) 103-125.
12. A.A. Lacey, Global blow-up of a nonlinear heat equation, Proc. Roy. Soc. Edinbugh 104A (1986) 161-167.
13. Y. Martel, Uniqueness of weak extremal solutions of nonlinear elliptic problems, Houston J. Math. 23 (1997) 161-168.
14. t - ∇u = g(u), Ann. Inst. Henry Poincaré, to appear.
15. I. Peral, J.L. Vazquez, On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term, Arch. Rational Mech. Anal. 129 (1995) 201-224.
16. M.H. Protter, H.F. Weinberger, Maximum Principles in Partial Differential Equations, Springer, Berlin, 1984, pp. 173-175.
17. p, Indiana Univ. Math. J. 29 (1980) 79-102.