-
Previous Article
On a new kind of convexity for solutions of parabolic problems
- DCDS-S Home
- This Issue
-
Next Article
Shape optimization for Monge-Ampère equations via domain derivative
Hot spots for the two dimensional heat equation with a rapidly decaying negative potential
1. | Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578 |
2. | Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, 599-8531 |
References:
[1] |
I. Chavel and L. Karp, Movement of hot spots in Riemannian manifolds, J. Analyse Math., 55 (1990), 271-286.
doi: doi:10.1007/BF02789205. |
[2] |
M. Escobedo and O. Kavian, Variational problems related to self-similar solutions of the heat equation, Nonlinear Anal. T. M. A., 11 (1987), 1103-1133.
doi: doi:10.1016/0362-546X(87)90001-0. |
[3] |
K. Ishige, Movement of hot spots on the exterior domain of a ball under the Neumann boundary condition, J. Differential Equations, 212 (2005), 394-431.
doi: doi:10.1016/j.jde.2004.11.002. |
[4] |
K. Ishige, Movement of hot spots on the exterior domain of a ball under the Dirichlet boundary condition, Adv. Differential Equations, 12 (2007), 1135-1166. |
[5] |
K. Ishige and Y. Kabeya, Large time behaviors of hot spots for the heat equation with a potential, J. Differential Equations, 244 (2008), 2934-2962; Corrigendum in J. Differential Equations, 245 (2008), 2352-2354.
doi: doi:10.1016/j.jde.2008.07.023. |
[6] |
K. Ishige and Y. Kabeya, Hot spots for the heat equation with a rapidly decaying negative potential, Adv. Differential Equations, 14 (2009), 643-662. |
[7] |
K. Ishige and Y. Kabeya, Large time behaviors of hot spots for the heat equation with a potential II: Positive potential case,, in preparation., ().
|
[8] |
S. Jimbo and S. Sakaguchi, Movement of hot spots over unbounded domains in $R^N$, J. Math. Anal. Appl., 182 (1994), 810-835.
doi: doi:10.1006/jmaa.1994.1123. |
[9] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc., Providence, 1968. |
show all references
References:
[1] |
I. Chavel and L. Karp, Movement of hot spots in Riemannian manifolds, J. Analyse Math., 55 (1990), 271-286.
doi: doi:10.1007/BF02789205. |
[2] |
M. Escobedo and O. Kavian, Variational problems related to self-similar solutions of the heat equation, Nonlinear Anal. T. M. A., 11 (1987), 1103-1133.
doi: doi:10.1016/0362-546X(87)90001-0. |
[3] |
K. Ishige, Movement of hot spots on the exterior domain of a ball under the Neumann boundary condition, J. Differential Equations, 212 (2005), 394-431.
doi: doi:10.1016/j.jde.2004.11.002. |
[4] |
K. Ishige, Movement of hot spots on the exterior domain of a ball under the Dirichlet boundary condition, Adv. Differential Equations, 12 (2007), 1135-1166. |
[5] |
K. Ishige and Y. Kabeya, Large time behaviors of hot spots for the heat equation with a potential, J. Differential Equations, 244 (2008), 2934-2962; Corrigendum in J. Differential Equations, 245 (2008), 2352-2354.
doi: doi:10.1016/j.jde.2008.07.023. |
[6] |
K. Ishige and Y. Kabeya, Hot spots for the heat equation with a rapidly decaying negative potential, Adv. Differential Equations, 14 (2009), 643-662. |
[7] |
K. Ishige and Y. Kabeya, Large time behaviors of hot spots for the heat equation with a potential II: Positive potential case,, in preparation., ().
|
[8] |
S. Jimbo and S. Sakaguchi, Movement of hot spots over unbounded domains in $R^N$, J. Math. Anal. Appl., 182 (1994), 810-835.
doi: doi:10.1006/jmaa.1994.1123. |
[9] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc., Providence, 1968. |
[1] |
Kazuhiro Ishige, Asato Mukai. Large time behavior of solutions of the heat equation with inverse square potential. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 4041-4069. doi: 10.3934/dcds.2018176 |
[2] |
James B. Kennedy, Jonathan Rohleder. On the hot spots of quantum graphs. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3029-3063. doi: 10.3934/cpaa.2021095 |
[3] |
Shigehiro Sakata, Yuta Wakasugi. Movement of time-delayed hot spots in Euclidean space for a degenerate initial state. Discrete and Continuous Dynamical Systems, 2020, 40 (5) : 2705-2738. doi: 10.3934/dcds.2020147 |
[4] |
Xiao-Hui Li, Huo-Jun Ruan. The "hot spots" conjecture on higher dimensional Sierpinski gaskets. Communications on Pure and Applied Analysis, 2016, 15 (1) : 287-297. doi: 10.3934/cpaa.2016.15.287 |
[5] |
Jesus Ildefonso Díaz, Jacqueline Fleckinger-Pellé. Positivity for large time of solutions of the heat equation: the parabolic antimaximum principle. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 193-200. doi: 10.3934/dcds.2004.10.193 |
[6] |
Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 |
[7] |
Cong He, Hongjun Yu. Large time behavior of the solution to the Landau Equation with specular reflective boundary condition. Kinetic and Related Models, 2013, 6 (3) : 601-623. doi: 10.3934/krm.2013.6.601 |
[8] |
Joana Terra, Noemi Wolanski. Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data. Discrete and Continuous Dynamical Systems, 2011, 31 (2) : 581-605. doi: 10.3934/dcds.2011.31.581 |
[9] |
Hiroshi Takeda. Large time behavior of solutions for a nonlinear damped wave equation. Communications on Pure and Applied Analysis, 2016, 15 (1) : 41-55. doi: 10.3934/cpaa.2016.15.41 |
[10] |
Nakao Hayashi, Elena I. Kaikina, Pavel I. Naumkin. Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 93-106. doi: 10.3934/dcds.1999.5.93 |
[11] |
Yueling Li, Yingchao Xie, Xicheng Zhang. Large deviation principle for stochastic heat equation with memory. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5221-5237. doi: 10.3934/dcds.2015.35.5221 |
[12] |
Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299 |
[13] |
Geonho Lee, Sangdong Kim, Young-Sam Kwon. Large time behavior for the full compressible magnetohydrodynamic flows. Communications on Pure and Applied Analysis, 2012, 11 (3) : 959-971. doi: 10.3934/cpaa.2012.11.959 |
[14] |
Ovidiu Cârjă, Alina Lazu. On the minimal time null controllability of the heat equation. Conference Publications, 2009, 2009 (Special) : 143-150. doi: 10.3934/proc.2009.2009.143 |
[15] |
Jin Takahashi, Eiji Yanagida. Time-dependent singularities in the heat equation. Communications on Pure and Applied Analysis, 2015, 14 (3) : 969-979. doi: 10.3934/cpaa.2015.14.969 |
[16] |
Chulan Zeng. Time analyticity of the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations. Communications on Pure and Applied Analysis, 2022, 21 (3) : 749-783. doi: 10.3934/cpaa.2021197 |
[17] |
Martin Burger, Marco Di Francesco. Large time behavior of nonlocal aggregation models with nonlinear diffusion. Networks and Heterogeneous Media, 2008, 3 (4) : 749-785. doi: 10.3934/nhm.2008.3.749 |
[18] |
Dongfen Bian, Boling Guo. Global existence and large time behavior of solutions to the electric-magnetohydrodynamic equations. Kinetic and Related Models, 2013, 6 (3) : 481-503. doi: 10.3934/krm.2013.6.481 |
[19] |
Jie Zhao. Large time behavior of solution to quasilinear chemotaxis system with logistic source. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1737-1755. doi: 10.3934/dcds.2020091 |
[20] |
Linlin Li, Bedreddine Ainseba. Large-time behavior of matured population in an age-structured model. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2561-2580. doi: 10.3934/dcdsb.2020195 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]