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Attractors for weakly damped beam equations with $p$-Laplacian
On global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients
| 1. | Dipartimento di Matematica e Informatica, Università di Cagliari, 09123 |
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References:
| [1] |
J.M. Ball, Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford 28, (1977), 473-486. |
| [2] |
H. Fujita, On the blowing up of solutions of the Cauchy problem for $u_t= \Delta u + u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo 13, (1966), 109-124. |
| [3] |
H. Kielhöfer, Halbgruppen und semilineare Anfangs-randwert-probleme, Manuscripta Math.12, (1974), 121-152. |
| [4] |
H.A. Levine, The role of the critical exponents in blow-up theorems, SIAM Review 32, (1990), 262-288. |
| [5] |
M. Marras, Bounds for blow-up time in nonlinear parabolic systems under various boundary conditions, Num. Funct. Anal. Optim. 32, (2011), 453- 468. |
| [6] |
M. Marras, S.Vernier Piro, Blow-up phenomena in reaction-diffusion systems, Discrete and Continuous Dynamical Systems 32, N. 11, (2012) 4001-4014. |
| [7] |
M. Marras, S.Vernier Piro, Bounds for blow-up time in nonlinear parabolic system, Discrete and Continuous Dynamical Systems, Suppl. 2011 (2011) 1025-1031. |
| [8] |
L.E. Payne, G.A. Philippin, Blow up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions, Proc. Amer. Math. Soc. 141, N. 7 (2013) 2309-2318. |
| [9] |
L.E. Payne, G.A. Philippin, P.W. Schaefer, Bounds for blow-up time in nonlinear parabolic problems, J.Math. Anal. Appl. 338 (2008), 438-447. |
| [10] |
L.E. Payne, G.A. Philippin, P.W. Schaefer, Blow-up phenomena for some nonlinear parabolic problems, Nonlinear Analysis. 69 (2008), 3495-3502. |
| [11] |
L.E. Payne, G.A. Philippin, S. Vernier-Piro, Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition I, Z. Angew. Math. Phys., 61 (2010), 971-978. |
| [12] |
L.E. Payne, G.A. Philippin, S. Vernier-Piro, Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition II, Nonlinear Analysis, 73 (2010), 971-978. |
| [13] |
L.E. Payne, P.W. Schaefer, Lower bounds for blow-up time in parabolic problems under Dirichlet boundary conditions, J. Math. Anal. Appl., 328 (2007), 1196-1205. |
| [14] |
L.E. Payne, P.W. Schaefer, Blow-up phenomena for some nonlinear parabolic systems, Int. J. of Pure and Applied Math., 42 (2008), 193-202. |
| [15] |
P. Quittner, P. Souplet, Superlinear parabolic problems. Blow-up, global existence and steady states, Birkhäuser Advanced Texts, Basel, (2007). |
| [16] |
G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl., 110 (1976), 353-372. |
| [17] |
F.B. Weissler, Local existence and nonexistence for semilinear parabolic equations in $L^p$, Indiana Univ. Math. J. 29 (1980), 79-102 . |
| [18] |
F.B. Weissler, Existence and nonexistence of global solutions for a heat equation, Israel J.Math. 38 (1981), n.1-2, 29-40. |
show all references
References:
| [1] |
J.M. Ball, Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford 28, (1977), 473-486. |
| [2] |
H. Fujita, On the blowing up of solutions of the Cauchy problem for $u_t= \Delta u + u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo 13, (1966), 109-124. |
| [3] |
H. Kielhöfer, Halbgruppen und semilineare Anfangs-randwert-probleme, Manuscripta Math.12, (1974), 121-152. |
| [4] |
H.A. Levine, The role of the critical exponents in blow-up theorems, SIAM Review 32, (1990), 262-288. |
| [5] |
M. Marras, Bounds for blow-up time in nonlinear parabolic systems under various boundary conditions, Num. Funct. Anal. Optim. 32, (2011), 453- 468. |
| [6] |
M. Marras, S.Vernier Piro, Blow-up phenomena in reaction-diffusion systems, Discrete and Continuous Dynamical Systems 32, N. 11, (2012) 4001-4014. |
| [7] |
M. Marras, S.Vernier Piro, Bounds for blow-up time in nonlinear parabolic system, Discrete and Continuous Dynamical Systems, Suppl. 2011 (2011) 1025-1031. |
| [8] |
L.E. Payne, G.A. Philippin, Blow up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions, Proc. Amer. Math. Soc. 141, N. 7 (2013) 2309-2318. |
| [9] |
L.E. Payne, G.A. Philippin, P.W. Schaefer, Bounds for blow-up time in nonlinear parabolic problems, J.Math. Anal. Appl. 338 (2008), 438-447. |
| [10] |
L.E. Payne, G.A. Philippin, P.W. Schaefer, Blow-up phenomena for some nonlinear parabolic problems, Nonlinear Analysis. 69 (2008), 3495-3502. |
| [11] |
L.E. Payne, G.A. Philippin, S. Vernier-Piro, Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition I, Z. Angew. Math. Phys., 61 (2010), 971-978. |
| [12] |
L.E. Payne, G.A. Philippin, S. Vernier-Piro, Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition II, Nonlinear Analysis, 73 (2010), 971-978. |
| [13] |
L.E. Payne, P.W. Schaefer, Lower bounds for blow-up time in parabolic problems under Dirichlet boundary conditions, J. Math. Anal. Appl., 328 (2007), 1196-1205. |
| [14] |
L.E. Payne, P.W. Schaefer, Blow-up phenomena for some nonlinear parabolic systems, Int. J. of Pure and Applied Math., 42 (2008), 193-202. |
| [15] |
P. Quittner, P. Souplet, Superlinear parabolic problems. Blow-up, global existence and steady states, Birkhäuser Advanced Texts, Basel, (2007). |
| [16] |
G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl., 110 (1976), 353-372. |
| [17] |
F.B. Weissler, Local existence and nonexistence for semilinear parabolic equations in $L^p$, Indiana Univ. Math. J. 29 (1980), 79-102 . |
| [18] |
F.B. Weissler, Existence and nonexistence of global solutions for a heat equation, Israel J.Math. 38 (1981), n.1-2, 29-40. |
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