-
Previous Article
Large deviations in expanding random dynamical systems
- DCDS Home
- This Issue
-
Next Article
Dimensions for recurrence times: topological and dynamical properties
Harmonic maps on complete manifolds
1. | Department of Mathematics, Southwest Missouri State University |
2. | Department of Applied Mathematics, University of Colorado at Boulder |
Our condition are: The Ricci curvature of M is bounded from below by a negative constant, M admits a positive Green’s function and
$ \int_M G(x, y)|\tau(h(y))|dV_y $ is bounded on each compact subset. $\qquad$ (1)
Here $\tau(h(x))$ is the tension field of the initial data $h(x)$.
Condition (1) is somewhat sharp as is shown by examples in the paper.
[1] |
Ze Li, Lifeng Zhao. Convergence to harmonic maps for the Landau-Lifshitz flows between two dimensional hyperbolic spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 607-638. doi: 10.3934/dcds.2019025 |
[2] |
Junyu Lin. Uniqueness of harmonic map heat flows and liquid crystal flows. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 739-755. doi: 10.3934/dcds.2013.33.739 |
[3] |
Y. Chen, S. Levine. The existence of the heat flow of H-systems. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 219-236. doi: 10.3934/dcds.2002.8.219 |
[4] |
Andrey Shishkov, Laurent Véron. Propagation of singularities of nonlinear heat flow in fissured media. Communications on Pure and Applied Analysis, 2013, 12 (4) : 1769-1782. doi: 10.3934/cpaa.2013.12.1769 |
[5] |
Karl Kunisch, Markus Müller. Uniform convergence of the POD method and applications to optimal control. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4477-4501. doi: 10.3934/dcds.2015.35.4477 |
[6] |
Zhong Tan, Qiuju Xu, Huaqiao Wang. Global existence and convergence rates for the compressible magnetohydrodynamic equations without heat conductivity. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 5083-5105. doi: 10.3934/dcds.2015.35.5083 |
[7] |
Luis Caffarelli, Fanghua Lin. Nonlocal heat flows preserving the L2 energy. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 49-64. doi: 10.3934/dcds.2009.23.49 |
[8] |
Eberhard Bänsch, Steffen Basting, Rolf Krahl. Numerical simulation of two-phase flows with heat and mass transfer. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2325-2347. doi: 10.3934/dcds.2015.35.2325 |
[9] |
Giulia Luise, Giuseppe Savaré. Contraction and regularizing properties of heat flows in metric measure spaces. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 273-297. doi: 10.3934/dcdss.2020327 |
[10] |
Shouwen Fang, Peng Zhu. Differential Harnack estimates for backward heat equations with potentials under geometric flows. Communications on Pure and Applied Analysis, 2015, 14 (3) : 793-809. doi: 10.3934/cpaa.2015.14.793 |
[11] |
J. R. L. Webb. Multiple positive solutions of some nonlinear heat flow problems. Conference Publications, 2005, 2005 (Special) : 895-903. doi: 10.3934/proc.2005.2005.895 |
[12] |
Youcef Amirat, Kamel Hamdache. Strong solutions to the equations of flow and heat transfer in magnetic fluids with internal rotations. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3289-3320. doi: 10.3934/dcds.2013.33.3289 |
[13] |
Mi-Ho Giga, Yoshikazu Giga, Takeshi Ohtsuka, Noriaki Umeda. On behavior of signs for the heat equation and a diffusion method for data separation. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2277-2296. doi: 10.3934/cpaa.2013.12.2277 |
[14] |
Andrew M. Zimmer. Compact asymptotically harmonic manifolds. Journal of Modern Dynamics, 2012, 6 (3) : 377-403. doi: 10.3934/jmd.2012.6.377 |
[15] |
Bo Chen, Youde Wang. Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional. Communications on Pure and Applied Analysis, 2021, 20 (1) : 319-338. doi: 10.3934/cpaa.2020268 |
[16] |
Bernd Ammann, Robert Lauter and Victor Nistor. Algebras of pseudodifferential operators on complete manifolds. Electronic Research Announcements, 2003, 9: 80-87. |
[17] |
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 |
[18] |
Yong Hong Wu, B. Wiwatanapataphee. Modelling of turbulent flow and multi-phase heat transfer under electromagnetic force. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 695-706. doi: 10.3934/dcdsb.2007.8.695 |
[19] |
Yasir Ali, Arshad Alam Khan. Exact solution of magnetohydrodynamic slip flow and heat transfer over an oscillating and translating porous plate. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 595-606. doi: 10.3934/dcdss.2018034 |
[20] |
Yaguang Wang, Shiyong Zhu. Blowup of solutions to the thermal boundary layer problem in two-dimensional incompressible heat conducting flow. Communications on Pure and Applied Analysis, 2020, 19 (6) : 3233-3244. doi: 10.3934/cpaa.2020141 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]