[1] H. Amann, P. Quittner:
Elliptic boundary value problems involving measures: existence, regularity, and multiplicity. Adv. Differ. Equ. 3 (1998), 753–813.
MR 1659273
[2] P. Baras, L. Cohen:
Complete blow-up after $T_{\max }$ for the solution of a semilinear heat equation. J. Funct. Anal. 71 (1987), 142–174.
MR 0879705
[3] P. Baras, M. Pierre:
Critère d’existence de solutions positives pour des équations semi-linéaires non monotones. Analyse Non Linéaire, Ann. Inst. H. Poincaré 2 (1985), 185–212.
MR 0797270 |
Zbl 0599.35073
[4] M.-F. Bidaut-Véron:
Initial blow-up for the solutions of a semilinear parabolic equation with source term. Equations aux dérivées partielles et applications, articles dédiés à Jacques-Louis Lions, Gauthier-Villars, Paris, 1998, pp. 189–198.
MR 1648222
[5] H. Brézis, R. E. L. Turner:
On a class of superlinear elliptic problems. Commun. Partial Differ. Equations 2 (1977), 601–614.
MR 0509489
[6] T. Cazenave, P.-L. Lions:
Solutions globales d’équations de la chaleur semi linéaires. Commun. Partial Differ. Equations 9 (1984), 955–978.
MR 0755928
[7] M. Chipot, M. Fila, P. Quittner:
Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Acta Math. Univ. Comen. 60 (1991), 35–103.
MR 1120596
[8] M. J. Esteban:
On periodic solutions of superlinear parabolic problems. Trans. Amer. Math. Soc. 293 (1986), 171–189.
MR 0814919 |
Zbl 0619.35058
[9] M. J. Esteban:
A remark on the existence of positive periodic solutions of superlinear parabolic problems. Proc. Amer. Math. Soc. 102 (1988), 131–136.
MR 0915730 |
Zbl 0653.35039
[10] C. Fermanian Kammerer, F. Merle, H. Zaag:
Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view. Math. Ann. 317 (2000), 347–387.
MR 1764243
[11] D. G. de Figueiredo, P.-L. Lions, R. D. Nussbaum:
A priori estimates and existence of positive solutions of semilinear elliptic equations. J. Math. Pures Appl. 61 (1982), 41–63.
MR 0664341
[12] M. Fila: Boundedness of global solutions of nonlinear parabolic problems. Proc. of the 4th European Conf. on Elliptic and Parabolic Problems, Rolduc 2001, to appear.
[13] M. Fila, P. Poláčik:
Global solutions of a semilinear parabolic equation. Adv. Differ. Equ. 4 (1999), 163–196.
MR 1674359
[14] M. Fila, P. Souplet, F. Weissler:
Linear and nonlinear heat equations in $L^q_\delta $ spaces and universal bounds for global solutions. Math. Ann. 320 (2001), 87–113.
MR 1835063
[15] S. Filippas, M. A. Herrero, J. J. L. Velázquez:
Fast blow-up mechanism for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity. R. Soc. Lond. Proc. Ser. A 456 (2000), 2957–2982.
MR 1843848
[16] V. Galaktionov, J. L. Vázquez: Continuation of blow-up solutions of nonlinear heat equations in several space dimensions. Commun. Pure Applied Math. 50 (1997), 1–67.
[17] B. Gidas, J. Spruck:
A priori bounds for positive solutions of nonlinear elliptic equations. Commun. Partial Differ. Equations 6 (1981), 883–901.
MR 0619749
[18] Y. Giga:
A bound for global solutions of semilinear heat equations. Commun. Math. Phys. 103 (1986), 415–421.
MR 0832917 |
Zbl 0595.35057
[19] Y. Giga, R. V. Kohn:
Characterizing blowup using similarity variables. Indiana Univ. Math. J. 36 (1987), 1–40.
MR 0876989
[20] M. A. Herrero, J. J. L. Velázquez:
Explosion de solutions d’équations paraboliques semilinéaires supercritiques. C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 141–145.
MR 1288393
[21] M. A. Herrero, J. J. L. Velázquez: A blow up result for semilinear heat equations in the supercritical case. Preprint.
[22] J. Húska:
Periodic solutions in superlinear parabolic problems. Acta Math. Univ. Comen (to appear).
MR 1943012
[23] H. A. Levine:
Some nonexistence and instability theorems for solutions of formally parabolic equations of the form $Pu_t=-Au+F(u)$. Arch. Rational Mech. Anal. 51 (1973), 371–386.
MR 0348216
[24] J. Matos, Ph. Souplet: Universal blow-up estimates and decay rates for a semilinear heat equation. Preprint.
[25] W.-M. Ni, P. E. Sacks, J. Tavantzis:
On the asymptotic behavior of solutions of certain quasilinear parabolic equations. J. Differ. Equations 54 (1984), 97–120.
MR 0756548
[26] R. D. Nussbaum:
Positive solutions of nonlinear elliptic boundary value problems. J. Math. Anal. Appl. 51 (1975), 461–482.
MR 0382850 |
Zbl 0304.35047
[27] S. I. Pohozaev:
Eigenfunctions of the equation $\Delta u+\lambda f(u)=0$. Soviet Math. Dokl. 5 (1965), 1408–1411.
MR 0192184
[28] P. Quittner:
A priori bounds for global solutions of a semilinear parabolic problem. Acta Math. Univ. Comen. 68 (1999), 195–203.
MR 1757788 |
Zbl 0940.35112
[29] P. Quittner:
A priori estimates of global solutions and multiple equilibria of a superlinear parabolic problem involving measure. Electronic J. Differ. Equations 2001 (2001), no. 29, 1–17.
MR 1836797
[30] P. Quittner:
Universal bound for global positive solutions of a superlinear parabolic problem. Math. Ann. 320 (2001), 299–305.
MR 1839765 |
Zbl 0981.35010
[31] P. Quittner:
Continuity of the blow-up time and a priori bounds for solutions in superlinear parabolic problems. Houston J. Math (to appear).
MR 1998164 |
Zbl 1034.35013
[32] P. Quittner:
Multiple equilibria, periodic solutions and a priori bounds for solutions in superlinear parabolic problems. NoDEA, Nonlinear Differ. Equations Appl (to appear).
MR 2210288 |
Zbl 1058.35120
[33] P. Quittner, Ph. Souplet:
A priori estimates of global solutions of superlinear parabolic problems without variational structure. Discrete Contin. Dyn. Systems (to appear).
MR 1974428
[34] P. Quittner, Ph. Souplet: Bounds of solutions of parabolic problems with nonlinear boundary conditions. In preparation.
[35] P. Quittner, Ph. Souplet, M. Winkler:
Initial blow-up rates and universal bounds for nonlinear heat equations. Preprint.
MR 2028111
[36] R. E. L. Turner:
A priori bounds for positive solutions of nonlinear elliptic equations in two variables. Duke Math. J. 41 (1974), 759–774.
MR 0364859 |
Zbl 0294.35033
[37] H. Zaag:
A remark on the energy blow-up behavior for nonlinear heat equations. Duke Math. J. 103 (2000), 545–556.
MR 1763658 |
Zbl 0971.35042