-
Previous Article
Instability of equatorial water waves in the $f-$plane
- DCDS Home
- This Issue
-
Next Article
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), 1013-1019.
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), 431-449.
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), 3596-3614.
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, ().
|
[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), 617-633.
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), 497-519.
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), 121-140.
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), 735-754.
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), 617-633.
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), 111-120.
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), 1013-1019.
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), 431-449.
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), 3596-3614.
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, ().
|
[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), 617-633.
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), 497-519.
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), 121-140.
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), 735-754.
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), 617-633.
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), 111-120.
doi: 10.1090/S0002-9939-96-03156-5. |
[1] |
Qiong Chen, Chunlai Mu, Zhaoyin Xiang. Blow-up and asymptotic behavior of solutions to a semilinear integrodifferential system. Communications on Pure and Applied Analysis, 2006, 5 (3) : 435-446. doi: 10.3934/cpaa.2006.5.435 |
[2] |
Guirong Liu, Yuanwei Qi. Sign-changing solutions of a quasilinear heat equation with a source term. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1389-1414. doi: 10.3934/dcdsb.2013.18.1389 |
[3] |
Weiwei Ao, Chao Liu. Asymptotic behavior of sign-changing radial solutions of a semilinear elliptic equation in $ \mathbb{R}^2 $ when exponent approaches $ +\infty $. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 5047-5077. doi: 10.3934/dcds.2020211 |
[4] |
Xiumei Deng, Jun Zhou. Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity. Communications on Pure and Applied Analysis, 2020, 19 (2) : 923-939. doi: 10.3934/cpaa.2020042 |
[5] |
Miaoqing Tian, Sining Zheng. Global boundedness versus finite-time blow-up of solutions to a quasilinear fully parabolic Keller-Segel system of two species. Communications on Pure and Applied Analysis, 2016, 15 (1) : 243-260. doi: 10.3934/cpaa.2016.15.243 |
[6] |
Mingyou Zhang, Qingsong Zhao, Yu Liu, Wenke Li. Finite time blow-up and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition. Electronic Research Archive, 2020, 28 (1) : 369-381. doi: 10.3934/era.2020021 |
[7] |
Yuya Tanaka, Tomomi Yokota. Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022075 |
[8] |
Yuta Wakasugi. Blow-up of solutions to the one-dimensional semilinear wave equation with damping depending on time and space variables. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3831-3846. doi: 10.3934/dcds.2014.34.3831 |
[9] |
Manuel del Pino, Monica Musso, Juncheng Wei, Yifu Zhou. Type Ⅱ finite time blow-up for the energy critical heat equation in $ \mathbb{R}^4 $. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3327-3355. doi: 10.3934/dcds.2020052 |
[10] |
Xiaoliang Li, Baiyu Liu. Finite time blow-up and global solutions for a nonlocal parabolic equation with Hartree type nonlinearity. Communications on Pure and Applied Analysis, 2020, 19 (6) : 3093-3112. doi: 10.3934/cpaa.2020134 |
[11] |
Jiaquan Liu, Xiangqing Liu, Zhi-Qiang Wang. Sign-changing solutions for a parameter-dependent quasilinear equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (5) : 1779-1799. doi: 10.3934/dcdss.2020454 |
[12] |
Bin Guo, Wenjie Gao. Finite-time blow-up and extinction rates of solutions to an initial Neumann problem involving the $p(x,t)-Laplace$ operator and a non-local term. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 715-730. doi: 10.3934/dcds.2016.36.715 |
[13] |
Alexander Gladkov. Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2053-2068. doi: 10.3934/cpaa.2017101 |
[14] |
Yohei Fujishima. On the effect of higher order derivatives of initial data on the blow-up set for a semilinear heat equation. Communications on Pure and Applied Analysis, 2018, 17 (2) : 449-475. doi: 10.3934/cpaa.2018025 |
[15] |
Asato Mukai, Yukihiro Seki. Refined construction of type II blow-up solutions for semilinear heat equations with Joseph–Lundgren supercritical nonlinearity. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4847-4885. doi: 10.3934/dcds.2021060 |
[16] |
Van Tien Nguyen. On the blow-up results for a class of strongly perturbed semilinear heat equations. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3585-3626. doi: 10.3934/dcds.2015.35.3585 |
[17] |
Frank Merle, Hatem Zaag. O.D.E. type behavior of blow-up solutions of nonlinear heat equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 435-450. doi: 10.3934/dcds.2002.8.435 |
[18] |
Gabriele Cora, Alessandro Iacopetti. Sign-changing bubble-tower solutions to fractional semilinear elliptic problems. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 6149-6173. doi: 10.3934/dcds.2019268 |
[19] |
Ahmad Z. Fino, Mohamed Ali Hamza. Blow-up of solutions to semilinear wave equations with a time-dependent strong damping. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022006 |
[20] |
Xiaoqiang Dai, Chao Yang, Shaobin Huang, Tao Yu, Yuanran Zhu. Finite time blow-up for a wave equation with dynamic boundary condition at critical and high energy levels in control systems. Electronic Research Archive, 2020, 28 (1) : 91-102. doi: 10.3934/era.2020006 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]