-
Previous Article
Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system
- DCDS Home
- This Issue
-
Next Article
Resurgence of inner solutions for perturbations of the McMillan map
Existence and non-existence of global solutions for a discrete semilinear heat equation
1. | University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8914, Japan, Japan |
References:
[1] |
J. Bebernes and D. Eberly, "Mathematical Problems from Combustion Theory," Appl. Math. Sci., 83, Springer-Verlag, New York, 1989. |
[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 Sect. A Math., 16 (1966), 109-124. |
[3] |
K. Hayakawa, On nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., 49 (1973), 503-505.
doi: 10.3792/pja/1195519254. |
[4] |
K. Kobayashi, T. Sirao and H. Tanaka, On the growing up problem for semilinear heat equations, J. Math. Soc. Japan, 29 (1977), 407-424.
doi: 10.2969/jmsj/02930407. |
[5] |
Howard A. Levine, The role of critical exponents in blowup theorems, SIAM Review, 32 (1990), 262-288.
doi: 10.1137/1032046. |
[6] |
P. Meier, On the critical exponent for reaction-diffusion equations, Arch. Rational Mech. Anal., 109 (1990), 63-71.
doi: 10.1007/BF00377979. |
[7] |
F. Spitzer, "Principles of Random Walk," Second edition, Graduate Texts in Mathematics, Vol. 34, Springer-Verlag, New York-Heidelberg, 1976. |
[8] |
F. B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math., 38 (1981), 29-40.
doi: 10.1007/BF02761845. |
show all references
References:
[1] |
J. Bebernes and D. Eberly, "Mathematical Problems from Combustion Theory," Appl. Math. Sci., 83, Springer-Verlag, New York, 1989. |
[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 Sect. A Math., 16 (1966), 109-124. |
[3] |
K. Hayakawa, On nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., 49 (1973), 503-505.
doi: 10.3792/pja/1195519254. |
[4] |
K. Kobayashi, T. Sirao and H. Tanaka, On the growing up problem for semilinear heat equations, J. Math. Soc. Japan, 29 (1977), 407-424.
doi: 10.2969/jmsj/02930407. |
[5] |
Howard A. Levine, The role of critical exponents in blowup theorems, SIAM Review, 32 (1990), 262-288.
doi: 10.1137/1032046. |
[6] |
P. Meier, On the critical exponent for reaction-diffusion equations, Arch. Rational Mech. Anal., 109 (1990), 63-71.
doi: 10.1007/BF00377979. |
[7] |
F. Spitzer, "Principles of Random Walk," Second edition, Graduate Texts in Mathematics, Vol. 34, Springer-Verlag, New York-Heidelberg, 1976. |
[8] |
F. B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math., 38 (1981), 29-40.
doi: 10.1007/BF02761845. |
[1] |
Pavol Quittner. The decay of global solutions of a semilinear heat equation. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 307-318. doi: 10.3934/dcds.2008.21.307 |
[2] |
Kazuhiro Ishige, Michinori Ishiwata. Global solutions for a semilinear heat equation in the exterior domain of a compact set. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 847-865. doi: 10.3934/dcds.2012.32.847 |
[3] |
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 |
[4] |
Peter Poláčik, Pavol Quittner. Entire and ancient solutions of a supercritical semilinear heat equation. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 413-438. doi: 10.3934/dcds.2020136 |
[5] |
Dominika Pilarczyk. Asymptotic stability of singular solution to nonlinear heat equation. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 991-1001. doi: 10.3934/dcds.2009.25.991 |
[6] |
Haruki Umakoshi. A semilinear heat equation with initial data in negative Sobolev spaces. Discrete and Continuous Dynamical Systems - S, 2021, 14 (2) : 745-767. doi: 10.3934/dcdss.2020365 |
[7] |
Christos Sourdis. A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart. Electronic Research Archive, 2021, 29 (5) : 2829-2839. doi: 10.3934/era.2021016 |
[8] |
Abdelaziz Khoutaibi, Lahcen Maniar, Omar Oukdach. Null controllability for semilinear heat equation with dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2022, 15 (6) : 1525-1546. doi: 10.3934/dcdss.2022087 |
[9] |
Yalçin Sarol, Frederi Viens. Time regularity of the evolution solution to fractional stochastic heat equation. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 895-910. doi: 10.3934/dcdsb.2006.6.895 |
[10] |
Claudianor O. Alves, Tahir Boudjeriou. Existence of solution for a class of heat equation in whole $ \mathbb{R}^N $. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4125-4144. doi: 10.3934/dcds.2021031 |
[11] |
Shota Sato, Eiji Yanagida. Forward self-similar solution with a moving singularity for a semilinear parabolic equation. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 313-331. doi: 10.3934/dcds.2010.26.313 |
[12] |
José F. Caicedo, Alfonso Castro. A semilinear wave equation with smooth data and no resonance having no continuous solution. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 653-658. doi: 10.3934/dcds.2009.24.653 |
[13] |
Xie Li, Zhaoyin Xiang. Existence and nonexistence of local/global solutions for a nonhomogeneous heat equation. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1465-1480. doi: 10.3934/cpaa.2014.13.1465 |
[14] |
Kazuhiro Ishige, Tatsuki Kawakami, Kanako Kobayashi. Global solutions for a nonlinear integral equation with a generalized heat kernel. Discrete and Continuous Dynamical Systems - S, 2014, 7 (4) : 767-783. doi: 10.3934/dcdss.2014.7.767 |
[15] |
Yongfu Wang. Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier-Stokes flows with vacuum. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4317-4333. doi: 10.3934/dcdsb.2020099 |
[16] |
Zefu Feng, Changjiang Zhu. Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3069-3097. doi: 10.3934/dcds.2019127 |
[17] |
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 |
[18] |
Soohyun Bae. Weighted $L^\infty$ stability of positive steady states of a semilinear heat equation in $\R^n$. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 823-837. doi: 10.3934/dcds.2010.26.823 |
[19] |
Ionuţ Munteanu. Design of boundary stabilizers for the non-autonomous cubic semilinear heat equation driven by a multiplicative noise. Evolution Equations and Control Theory, 2020, 9 (3) : 795-816. doi: 10.3934/eect.2020034 |
[20] |
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 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]