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On the Cauchy problem for a generalized Camassa-Holm equation
Blow up of solutions of semilinear heat equations in non radial domains of $\mathbb{R}^2$
1. | Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientica 1, 00133 Roma, Italy |
2. | Dipartimento di Matematica e Fisica, Seconda Università di Napoli, V.le Lincoln 5, 81100 Caserta, Italy |
References:
[1] |
Adimurthi and M. Grossi, Asymptotic estimates for a two dimensional problem with polynomial nonlinearity,, Proc. Amer. Math. Soc., 132 (2004), 1013.
doi: 10.1090/S0002-9939-03-07301-5. |
[2] |
T. Cazenave, F. Dickstein and F. B. Weissler, Sign-changing stationary solutions and blow up for the nonlinear heat equation in a ball,, Math Ann., 344 (2009), 431.
doi: 10.1007/s00208-008-0312-6. |
[3] |
F. De Marchis, I. Ianni and F. Pacella, Sign changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations,, Journal of Differential Equations, 254 (2013), 3596.
doi: 10.1016/j.jde.2013.01.037. |
[4] |
F. De Marchis, I. Ianni and F. Pacella, Asymptotic analysis and sign changing bubble towers for Lane-Emden problems,, accepted for publication in Journal of the European Mathematical Society, (). Google Scholar |
[5] |
F. Dickstein, F. Pacella and B. Sciunzi, Sign-changing stationary solutions and blow up for the nonlinear heat equation in dimension two,, Journal of Evolution Equation, 14 (2014), 617.
doi: 10.1007/s00028-014-0230-x. |
[6] |
P. Esposito, M. Musso and A. Pistoia, On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity,, Proc. Lond. Math. Soc., 94 (2007), 497.
doi: 10.1112/plms/pdl020. |
[7] |
M. Grossi, C. Grumiau and F. Pacella, Lane Emden problems: Asymptotic behavior of low energy nodal solutions,, Ann. Inst. H. Poincare Anal. Non Lineaire, 30 (2013), 121.
doi: 10.1016/j.anihpc.2012.06.005. |
[8] |
M. Grossi, C. Grumiau and F. Pacella, Lane Emden problems with large exponents and singular Liouville equations,, Journal Math. Pure and Appl., 101 (2014), 735.
doi: 10.1016/j.matpur.2013.06.011. |
[9] |
V. Marino, F. Pacella and B. Sciunzi, Blow-up of solutions of semilinear heat equations in general domains,, Comm. Cont. Math., 14 (2014), 617.
doi: 10.1142/S0219199713500429. |
[10] |
P. Quittner and P. Souplet, Superlinear Parabolic Problems,, Birkhäuser Basel-Boston-Berlin, (2007).
|
[11] |
X. Ren and J. Wei, Single-point condensation and least-energy solutions,, Proc. Amer. Math. Soc., 124 (1996), 111.
doi: 10.1090/S0002-9939-96-03156-5. |
show all references
References:
[1] |
Adimurthi and M. Grossi, Asymptotic estimates for a two dimensional problem with polynomial nonlinearity,, Proc. Amer. Math. Soc., 132 (2004), 1013.
doi: 10.1090/S0002-9939-03-07301-5. |
[2] |
T. Cazenave, F. Dickstein and F. B. Weissler, Sign-changing stationary solutions and blow up for the nonlinear heat equation in a ball,, Math Ann., 344 (2009), 431.
doi: 10.1007/s00208-008-0312-6. |
[3] |
F. De Marchis, I. Ianni and F. Pacella, Sign changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations,, Journal of Differential Equations, 254 (2013), 3596.
doi: 10.1016/j.jde.2013.01.037. |
[4] |
F. De Marchis, I. Ianni and F. Pacella, Asymptotic analysis and sign changing bubble towers for Lane-Emden problems,, accepted for publication in Journal of the European Mathematical Society, (). Google Scholar |
[5] |
F. Dickstein, F. Pacella and B. Sciunzi, Sign-changing stationary solutions and blow up for the nonlinear heat equation in dimension two,, Journal of Evolution Equation, 14 (2014), 617.
doi: 10.1007/s00028-014-0230-x. |
[6] |
P. Esposito, M. Musso and A. Pistoia, On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity,, Proc. Lond. Math. Soc., 94 (2007), 497.
doi: 10.1112/plms/pdl020. |
[7] |
M. Grossi, C. Grumiau and F. Pacella, Lane Emden problems: Asymptotic behavior of low energy nodal solutions,, Ann. Inst. H. Poincare Anal. Non Lineaire, 30 (2013), 121.
doi: 10.1016/j.anihpc.2012.06.005. |
[8] |
M. Grossi, C. Grumiau and F. Pacella, Lane Emden problems with large exponents and singular Liouville equations,, Journal Math. Pure and Appl., 101 (2014), 735.
doi: 10.1016/j.matpur.2013.06.011. |
[9] |
V. Marino, F. Pacella and B. Sciunzi, Blow-up of solutions of semilinear heat equations in general domains,, Comm. Cont. Math., 14 (2014), 617.
doi: 10.1142/S0219199713500429. |
[10] |
P. Quittner and P. Souplet, Superlinear Parabolic Problems,, Birkhäuser Basel-Boston-Berlin, (2007).
|
[11] |
X. Ren and J. Wei, Single-point condensation and least-energy solutions,, Proc. Amer. Math. Soc., 124 (1996), 111.
doi: 10.1090/S0002-9939-96-03156-5. |
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