no. 4
The preventive effect of the convection and of the diffusion in the blow-up phenomenon for parabolic equations
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 4, pp. 533-541 
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     author = {Tersenov, Alkis S},
     title = {The preventive effect of the convection and of the diffusion in the blow-up phenomenon for parabolic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {533--541},
     year = {2004},
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     volume = {21},
     number = {4},
     doi = {10.1016/j.anihpc.2003.10.001},
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     zbl = {1060.35047},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2003.10.001/}
}
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Tersenov, Alkis S. The preventive effect of the convection and of the diffusion in the blow-up phenomenon for parabolic equations. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 4, pp. 533-541. doi: 10.1016/j.anihpc.2003.10.001

[1] Aguirre J, Escobedo M, On the blow-up of a convective reaction diffusion equation, Proc. Roy. Soc. Edinburgh Sect. A 123 (3) (1993) 433-460. | Zbl | MR

[2] Bandle C, Levine H.A, Fujita type phenomena for reaction-diffusion equations with convection like terms, Differential Integral Equations 7 (5-6) (1994) 1169-1193. | Zbl | MR

[3] Chipot M, Weissler F.B, Some blowup results for a nonlinear parabolic equation with a gradient term, SIAM J. Math. Anal. 20 (1989) 886-907. | Zbl | MR

[4] Chlebik M, Fila M, Quittner P, Blow-up of positive solutions of a semilinear parabolic equation with a gradient term, Dyn. Cont. Discrete Impuls. Syst. Ser. A Math. Anal. 10 (4) (2003) 525-537. | Zbl | MR

[5] Fila M, Remarks on blow up for a nonlinear parabolic equation with gradient term, Proc. Amer. Math. Soc. 111 (1991) 795-801. | Zbl | MR

[6] Kawohl B, Peletier L.A, Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z. 202 (1989) 207-217. | Zbl | MR

[7] Quittner P, Blow-up for semilinear parabolic equations with a gradient term, Math. Mehods Appl. Sci. 14 (1991) 413-417. | Zbl | MR

[8] Quittner P, On global existence and stationary solutions for two classes of semilinear parabolic problems, Comment. Math. Univ. Carolin. 34 (1) (1993) 105-124. | Zbl | MR

[9] Ladyzhenskaja O.A, Solonnikov V.A, Uraltseva N.N, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, Amer. Math. Society, Providence, RI, 1968.

[10] Levine H.A, Payne L.E, Sacks P.E, Straughan B, Analysis of a convective reaction-diffusion equation, SIAM J. Math. Anal. 20 (1) (1989) 133-147. | Zbl | MR

[11] Lieberman G, Second Order Parabolic Equations, World Scientific, River Edge, NJ, 1996. | Zbl | MR

[12] Samarskii A.A, Galaktionov V.A, Kurdjumov S.P, Mikhailov A.P, Blow-up in quasilinear parabolic equations, in: de Gruyter Expositions Math., vol. 19, de Gruyter, Berlin, 1995, pp. 535. | Zbl | MR

[13] Souplet Ph, Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications, Math. Mehods Appl. Sci. 19 (1996) 1317-1333. | Zbl | MR

[14] Souplet Ph, Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions, Differential Integral Equations 15 (2) (2002) 237-256. | Zbl | MR

[15] Souplet Ph, Weissler F.B, Self-similar subsolutions and blow-up for nonlinear parabolic equations, J. Math. Anal. Appl. 212 (1997) 60-74. | Zbl | MR

[16] Souplet Ph, Weissler F.B, Poincare inequality and global solutions of a nonlinear parabolic equations, Ann. Inst. H. Poincaré Anal. Nonlineaire 16 (3) (1999) 337-373. | Zbl | MR | Numdam

[17] Tersenov Al, On the first boundary value problem for quasilinear parabolic equations with two independent variables, Arch. Ration. Mech. Anal. 152 (2000) 81-92. | Zbl | MR

[18] Tersenov Al, Tersenov Ar, Global solvability for a class of quasilinear parabolic equations, Indiana Univ. Math. J. 50 (4) (2001) 1899-1913. | Zbl | MR

[19] Tersenov Al, Estimate of the solution of the Dirichlet problem for parabolic equations and applications, J. Math. Anal. Appl. 273 (1) (2002) 206-216. | Zbl | MR

[20] Tersenov Al, Tersenov Ar, On the Cauchy problem for a class of quasilinear parabolic equations, Ann. Mat. Pura Appl. 182 (3) (2003) 325-336. | Zbl | MR

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