-
1
-
-
84971116414
-
On the blow up of solutions for a convective reaction diffusion equation
-
J. Aguirre, M. Escobedo, On the blow up of solutions for a convective reaction diffusion equation, Proc. Roy. Soc. Edinburgh., 123A, 3 (1993), 433–460.
-
(1993)
Proc. Roy. Soc. Edinburgh.
, vol.123A
, Issue.3
, pp. 433-460
-
-
Aguirre, J.1
Escobedo, M.2
-
2
-
-
84968519124
-
The formation of the dead core in parabolic reaction-diffusion problems
-
C. Bandle, I. Stakgold, The formation of the dead core in parabolic reaction-diffusion problems, Trans. Amer. Math. Soc., 286 (1984), 275–293.
-
(1984)
Trans. Amer. Math. Soc.
, vol.286
, pp. 275-293
-
-
Bandle, C.1
Stakgold, I.2
-
3
-
-
0001590177
-
max for the solution of a semilinear heat equation
-
max for the solution of a semilinear heat equation, J. Funct. Anal., 71 (1987), 142–174.
-
(1987)
J. Funct. Anal.
, vol.71
, pp. 142-174
-
-
Baras, P.1
Cohen, L.2
-
5
-
-
1642367710
-
Gradient bounds for solutions of semilinear parabolic equations without Bernstein’s quadratic condition
-
J.-Ph. Bartier, Ph. Souplet, Gradient bounds for solutions of semilinear parabolic equations without Bernstein’s quadratic condition, C.R. Acad. Sc. Paris, 338 (2004), 533–538.
-
(2004)
C.R. Acad. Sc. Paris
, vol.338
, pp. 533-538
-
-
Bartier, J.-P.1
Souplet, P.2
-
6
-
-
0024719715
-
Characterization of blow-up for a semilinear heat equation with a convection term
-
J. Bebernes, D. Eberly, Characterization of blow-up for a semilinear heat equation with a convection term, Quart. J. Mech. Appl. Mech., 42 (1989) 447–456.
-
(1989)
Quart. J. Mech. Appl. Mech.
, vol.42
, pp. 447-456
-
-
Bebernes, J.1
Eberly, D.2
-
7
-
-
0041417708
-
Initial blow-up for the solutions of a semilinear parabolic equation with source term
-
Gauthier-Villars, Paris
-
M.-F. Bidaut-Véron, Initial blow-up for the solutions of a semilinear parabolic equation with source term, in: Equations aux dérivées partielles et applications, articles dédiés à Jacques-Louis Lions. Gauthier-Villars, Paris, 1998, pp. 189–198.
-
(1998)
Equations Aux dérivées Partielles Et Applications, Articles dédiés à Jacques-Louis Lions
, pp. 189-198
-
-
Bidaut-Véron, M.-F.1
-
8
-
-
0000877190
-
Universality in blow-up for nonlinear heat equations
-
J. Bricmont, A. Kupiainen, Universality in blow-up for nonlinear heat equations, Nonlinearity, 7 (1994), 539–575.
-
(1994)
Nonlinearity
, vol.7
, pp. 539-575
-
-
Bricmont, J.1
Kupiainen, A.2
-
9
-
-
0000581856
-
Some blow up results for a nonlinear parabolic problem with a gradient term
-
M. Chipot, F.B. Weissler, Some blow up results for a nonlinear parabolic problem with a gradient term, SIAM J. Math. Anal., 20 (1989), 886–907.
-
(1989)
SIAM J. Math. Anal.
, vol.20
, pp. 886-907
-
-
Chipot, M.1
Weissler, F.B.2
-
10
-
-
0002499851
-
From critical exponents to blowup rates for parabolic problems
-
M. Chlebik, M. Fila, From critical exponents to blowup rates for parabolic problems, Rend. Mat. Appl., Ser. VII, 19 (1999), 449–470.
-
(1999)
Rend. Mat. Appl., Ser
, vol.7
, Issue.19
, pp. 449-470
-
-
Chlebik, M.1
Fila, M.2
-
11
-
-
2942549225
-
Blowup of positive solutions of a semilinear parabolic equation with a gradient term
-
M. Chlebik, M. Fila, P. Quittner, Blowup of positive solutions of a semilinear parabolic equation with a gradient term, Dyn. Contin. Discrete Impulsive Syst. Ser. A, 10 (2003), 525–537.
-
(2003)
Dyn. Contin. Discrete Impulsive Syst. Ser. A
, vol.10
, pp. 525-537
-
-
Chlebik, M.1
Fila, M.2
Quittner, P.3
-
12
-
-
51249168390
-
Stabilization of solutions of a nonlinear parabolic equation with a gradient term
-
K. Deng, Stabilization of solutions of a nonlinear parabolic equation with a gradient term, Math. Z., 216 (1994), 147–155.
-
(1994)
Math. Z.
, vol.216
, pp. 147-155
-
-
Deng, K.1
-
13
-
-
84968503362
-
Remarks on blow up for a nonlinear parabolic equation with a gradient term
-
M. Fila, Remarks on blow up for a nonlinear parabolic equation with a gradient term, Proc. Amer. Math. Soc., 111 (1991), 795–801.
-
(1991)
Proc. Amer. Math. Soc.
, vol.111
, pp. 795-801
-
-
Fila, M.1
-
16
-
-
0038563718
-
The blow-up rate for semilinear parabolic problems on general domains
-
M. Fila, Ph. Souplet, The blow-up rate for semilinear parabolic problems on general domains, Nonlinear Differ. Eq. and Appl. NoDEA, 8 (2001), 473–480.
-
(2001)
Nonlinear Differ. Eq. and Appl. Nodea
, vol.8
, pp. 473-480
-
-
Fila, M.1
Souplet, P.2
-
17
-
-
0010816767
-
Quenching profiles for one-dimensional semilinear heat equations
-
S. Filippas, J.-S. Guo, Quenching profiles for one-dimensional semilinear heat equations, Quart. Appl. Math., 51 (1993), 713–729.
-
(1993)
Quart. Appl. Math.
, vol.51
, pp. 713-729
-
-
Filippas, S.1
Guo, J.-S.2
-
18
-
-
0011234286
-
Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
-
S. Filippas, M.A. Herrero, J.J.L. Velázquez, Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity, Proc. R. Soc. Lond. A, 456 (2000), 2957–2982.
-
(2000)
Proc. R. Soc. Lond. A
, vol.456
, pp. 2957-2982
-
-
Filippas, S.1
Herrero, M.A.2
Velázquez, J.J.L.3
-
19
-
-
0023366191
-
Extinction properties of semilinear heat equations with strong absorption
-
A. Friedman, M.A. Herrero, Extinction properties of semilinear heat equations with strong absorption, J. Math. Anal. Appl., 124 (1987), 530–546.
-
(1987)
J. Math. Anal. Appl.
, vol.124
, pp. 530-546
-
-
Friedman, A.1
Herrero, M.A.2
-
20
-
-
0000546335
-
Blowup of positive solutions of semilinear heat equations
-
A. Friedman, J.B. McLeod, Blowup of positive solutions of semilinear heat equations, Indiana Univ. Math. J., 34 (1985), 425–447.
-
(1985)
Indiana Univ. Math. J.
, vol.34
, pp. 425-447
-
-
Friedman, A.1
McLeod, J.B.2
-
21
-
-
0010505120
-
Application of new comparison theorems to the investigation of unbounded solutions of nonlinear parabolic equations (Russian)
-
(Engl. transl.: Differ. Equations, 22 (1986), 809–815.)
-
V.A. Galaktionov, S. Posashkov, Application of new comparison theorems to the investigation of unbounded solutions of nonlinear parabolic equations (Russian), Differ. Uravn., 22 (1986), 1165–1173. (Engl. transl.: Differ. Equations, 22 (1986), 809–815.)
-
(1986)
Differ. Uravn.
, vol.22
, pp. 1165-1173
-
-
Galaktionov, V.A.1
Posashkov, S.2
-
22
-
-
21844506741
-
Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations
-
V.A. Galaktionov, J.L. Vázquez, Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations, Arch. Rational Mech. Anal., 129 (1995), 225–244.
-
(1995)
Arch. Rational Mech. Anal.
, vol.129
, pp. 225-244
-
-
Galaktionov, V.A.1
Vázquez, J.L.2
-
23
-
-
0030147090
-
Blowup for quasilinear heat equations described by means of nonlinear Hamilton-Jacobi equations
-
V.A. Galaktionov, J.L. Vázquez, Blowup for quasilinear heat equations described by means of nonlinear Hamilton-Jacobi equations, J. Differ. Equations, 127 (1996), 1–40.
-
(1996)
J. Differ. Equations
, vol.127
, pp. 1-40
-
-
Galaktionov, V.A.1
Vázquez, J.L.2
-
25
-
-
0001464964
-
A bound for global solutions of semilinear heat equations
-
Y. Giga, A bound for global solutions of semilinear heat equations, Comm. Math. Phys., 103 (1986), 415–421.
-
(1986)
Comm. Math. Phys.
, vol.103
, pp. 415-421
-
-
Giga, Y.1
-
26
-
-
84990616610
-
Asymptotically self-similar blow-up of semilinear heat equations
-
Y. Giga, R.V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math., 38 (1985), 297–319.
-
(1985)
Comm. Pure Appl. Math.
, vol.38
, pp. 297-319
-
-
Giga, Y.1
Kohn, R.V.2
-
27
-
-
0000332576
-
Characterizing blowup using similarity variables
-
Y. Giga, R.V. Kohn, Characterizing blowup using similarity variables, Indiana Univ. Math. J., 36 (1987), 1–40.
-
(1987)
Indiana Univ. Math. J.
, vol.36
, pp. 1-40
-
-
Giga, Y.1
Kohn, R.V.2
-
28
-
-
84990575181
-
Nondegeneracy of blowup for semilinear heat equations
-
Y. Giga, R.V. Kohn, Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math., 42 (1989), 845–884.
-
(1989)
Comm. Pure Appl. Math.
, vol.42
, pp. 845-884
-
-
Giga, Y.1
Kohn, R.V.2
-
29
-
-
3042688935
-
Blow up rate for semilinear heat equations with subcritical nonlinearity
-
Y. Giga, S. Matsui, S. Sasayama, Blow up rate for semilinear heat equations with subcritical nonlinearity, Indiana Univ. Math. J., 53 (2004), 483–514.
-
(2004)
Indiana Univ. Math. J.
, vol.53
, pp. 483-514
-
-
Giga, Y.1
Matsui, S.2
Sasayama, S.3
-
30
-
-
4744344778
-
On blow-up rate for sign-changing solutions in a convex domain
-
Y. Giga, S. Matsui, S. Sasayama, On blow-up rate for sign-changing solutions in a convex domain, Math. Methods Appl. Sci., 27 (2004), 1771–1782.
-
(2004)
Math. Methods Appl. Sci.
, vol.27
, pp. 1771-1782
-
-
Giga, Y.1
Matsui, S.2
Sasayama, S.3
-
31
-
-
85045504394
-
Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up
-
J.-S. Guo, Ph. Souplet, Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up, Math. Ann., to appear.
-
Math. Ann., to Appear
-
-
Guo, J.-S.1
Souplet, P.2
-
32
-
-
0000172301
-
Explosion de solutions des équations paraboliques semilinéaires supercritiques
-
M.A. Herrero, J.J.L. Velazquez, Explosion de solutions des équations paraboliques semilinéaires supercritiques, C. R. Acad. Sc. Paris Série I, 319 (1994), 141– 145.
-
(1994)
C. R. Acad. Sc. Paris Série I
, vol.319
, pp. 141-145
-
-
Herrero, M.A.1
Velazquez, J.J.L.2
-
33
-
-
0001091789
-
Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition
-
B. Hu, Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition, Differ. Integral Equations, 9 (1996), 891–901.
-
(1996)
Differ. Integral Equations
, vol.9
, pp. 891-901
-
-
Hu, B.1
-
34
-
-
0000885478
-
Remarks on blowup and dead cores for nonlinear parabolic equations
-
B. Kawohl, L. Peletier, Remarks on blowup and dead cores for nonlinear parabolic equations, Math. Z., 202 (1989), 207–217.
-
(1989)
Math. Z.
, vol.202
, pp. 207-217
-
-
Kawohl, B.1
Peletier, L.2
-
35
-
-
84974378755
-
Global blowup of a nonlinear heat equation
-
A.A. Lacey, Global blowup of a nonlinear heat equation, Proc. Royal Soc. Edinburgh, 104 (1986), 161–167.
-
(1986)
Proc. Royal Soc. Edinburgh
, vol.104
, pp. 161-167
-
-
Lacey, A.A.1
-
36
-
-
0003690985
-
Linear and Quasilinear Equations of Parabolic Type
-
O. Ladyzenskaya, V.A. Solonnikov, N.N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. Translations, Providence, RI, 1967.
-
(1967)
Amer. Math. Soc. Translations, Providence, RI
-
-
Ladyzenskaya, O.1
Solonnikov, V.A.2
Uralceva, N.N.3
-
37
-
-
0005885270
-
A blowup result for the critical exponent in cones
-
H.A. Levine, P. Meier, A blowup result for the critical exponent in cones, Israel J. Math., 67 (1989), 129–136.
-
(1989)
Israel J. Math.
, vol.67
, pp. 129-136
-
-
Levine, H.A.1
Meier, P.2
-
38
-
-
0000350812
-
Analysis of convective reaction-diffusion equation (II
-
H.A. Levine, L.N. Payne, P.E. Sacks, B. Straughan, Analysis of convective reaction-diffusion equation (II), SIAM J. Math. Anal., 20 (1989), 133–147.
-
(1989)
SIAM J. Math. Anal.
, vol.20
, pp. 133-147
-
-
Levine, H.A.1
Payne, L.N.2
Sacks, P.E.3
Straughan, B.4
-
39
-
-
7044224827
-
On nonexistence of type II blow-up for a supercritical nonlinear heat equation
-
H. Matano, F. Merle, On nonexistence of type II blow-up for a supercritical nonlinear heat equation, Commun. Pure Appl. Math., 57 (2004), 1494–1541.
-
(2004)
Commun. Pure Appl. Math.
, vol.57
, pp. 1494-1541
-
-
Matano, H.1
Merle, F.2
-
40
-
-
7044220297
-
Self-similar blow up patterns in supercritical semilinear heat equations
-
J. Matos, Self-similar blow up patterns in supercritical semilinear heat equations, Commun. Appl. Anal., 5 (2001), 455–483.
-
(2001)
Commun. Appl. Anal.
, vol.5
, pp. 455-483
-
-
Matos, J.1
-
41
-
-
0142259302
-
Universal blow-up rates for a semilinear heat equation and applications
-
J. Matos, Ph. Souplet, Universal blow-up rates for a semilinear heat equation and applications, Advances Differ. Equations, 8 (2003), 615–639.
-
(2003)
Advances Differ. Equations
, vol.8
, pp. 615-639
-
-
Matos, J.1
Souplet, P.2
-
42
-
-
0042515249
-
Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition
-
N. Mizoguchi, Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition, J. Differ. Equations, 193 (2003), 212–238.
-
(2003)
J. Differ. Equations
, vol.193
, pp. 212-238
-
-
Mizoguchi, N.1
-
43
-
-
0003187917
-
Single point blow-up for a general semilinear heat equation
-
C. Mueller, F.B. Weissler, Single point blow-up for a general semilinear heat equation, Indiana Univ. Math. J., 34 (1985), 881–913.
-
(1985)
Indiana Univ. Math. J.
, vol.34
, pp. 881-913
-
-
Mueller, C.1
Weissler, F.B.2
-
44
-
-
84951416437
-
Existence of solutions of quenching problems
-
D. Phillips, Existence of solutions of quenching problems, Appl. Anal., 24 (1987), 253–264.
-
(1987)
Appl. Anal.
, vol.24
, pp. 253-264
-
-
Phillips, D.1
-
45
-
-
85045527731
-
-
unpublished manuscript
-
M. Pierre, unpublished manuscript (2003).
-
(2003)
-
-
Pierre, M.1
-
46
-
-
0041737982
-
Continuity of the blow-up time and a priori bounds for solutions in superlinear parabolic problems
-
P. Quittner, Continuity of the blow-up time and a priori bounds for solutions in superlinear parabolic problems, Houston J. Math., 29 (2003), 757–799.
-
(2003)
Houston J. Math.
, vol.29
, pp. 757-799
-
-
Quittner, P.1
-
48
-
-
0038784323
-
A priori estimates of global solutions of superlinear parabolic problems without variational structure
-
P. Quittner, Ph. Souplet, A priori estimates of global solutions of superlinear parabolic problems without variational structure, Discrete Contin. Dyn. Syst., 9 (2003), 1277–1292.
-
(2003)
Discrete Contin. Dyn. Syst.
, vol.9
, pp. 1277-1292
-
-
Quittner, P.1
Souplet, P.2
-
49
-
-
52549103290
-
Recent results and open problems on parabolic equations with gradient nonlinearities
-
Ph. Souplet, Recent results and open problems on parabolic equations with gradient nonlinearities, Electronic J. Differ. Equations, Vol. 2001 (2001), No. 20, pp. 1–19.
-
(2001)
Electronic J. Differ. Equations
, vol.2001
, Issue.20
, pp. 1-19
-
-
Souplet, P.1
-
50
-
-
0005794877
-
Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions
-
Ph. Souplet, Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions, Differ. Integral Equations, 15 (2002), 237–256.
-
(2002)
Differ. Integral Equations
, vol.15
, pp. 237-256
-
-
Souplet, P.1
-
52
-
-
0347340615
-
Blow-up rates for nonlinear heat equations with gradient terms and for parabolic inequalities
-
Ph. Souplet, S. Tayachi, Blow-up rates for nonlinear heat equations with gradient terms and for parabolic inequalities, Colloq. Math., 88 (2001), 135–154.
-
(2001)
Colloq. Math.
, vol.88
, pp. 135-154
-
-
Souplet, P.1
Tayachi, S.2
-
53
-
-
0000126964
-
Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term
-
Ph. Souplet, S. Tayachi, F.B. Weissler, Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term, Indiana Univ. Math. J., 48 (1996), 655–682.
-
(1996)
Indiana Univ. Math. J.
, vol.48
, pp. 655-682
-
-
Souplet, P.1
Tayachi, S.2
Weissler, F.B.3
-
54
-
-
0031195373
-
Self-similar sub-solutions and blow-up for nonlinear parabolic equations
-
Ph. Souplet, F.B. Weissler, Self-similar sub-solutions and blow-up for nonlinear parabolic equations, J. Math. Anal. Appl., 212 (1997), 60–74.
-
(1997)
J. Math. Anal. Appl.
, vol.212
, pp. 60-74
-
-
Souplet, P.1
Weissler, F.B.2
-
55
-
-
0012103230
-
Poincaré’s inequality and global solutions of a nonlinear parabolic equation
-
Ph. Souplet, F.B. Weissler, Poincaré’s inequality and global solutions of a nonlinear parabolic equation, Ann. Inst. H. Poincaré, Analyse non linéaire, 16 (1999), 337–373.
-
(1999)
Ann. Inst. H. Poincaré, Analyse Non linéaire
, vol.16
, pp. 337-373
-
-
Souplet, P.1
Weissler, F.B.2
-
56
-
-
0002145775
-
Blow up for semilinear parabolic equations
-
(eds.), John Wiley & Sons
-
J.J.L. Velázquez, Blow up for semilinear parabolic equations, in: Research in applied mathematics, Recent advances in partial differential equations, M.A. Herrero and E. Zuazua (eds.), John Wiley & Sons, 1994, pp. 131–145.
-
(1994)
Research in Applied Mathematics, Recent Advances in Partial Differential Equations, M.A. Herrero and E. Zuazua
, pp. 131-145
-
-
Velázquez, J.J.L.1
-
57
-
-
38249006022
-
The Lipschitz continuity of the interface in the heat equation with strong absorption
-
H.-M. Yin, The Lipschitz continuity of the interface in the heat equation with strong absorption, Nonlinear Anal., 20 (1993), 413–416.
-
(1993)
Nonlinear Anal
, vol.20
, pp. 413-416
-
-
Yin, H.-M.1
|