-
Previous Article
Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics
- KRM Home
- This Issue
-
Next Article
Oscillatory behavior of Asymptotic-Preserving splitting methods for a linear model of diffusive relaxation
A kinetic model for grain growth
| 1. | Hochschulrechenzentrum der Universität Bonn, Wegelerstraße 6, D-53115 Bonn, Germany |
| 2. | University of Oxford, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, United Kingdom |
| 3. | Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB |
| 4. | Instituto de Ciencias Mathemáticas (CSIC-UAM-UC3M-UCM), Serrano 123, 28006 Madrid, Spain |
We prove existence of solutions by approximation with finite dimensional systems. Key ingredients in passing to the limit are suitable super--solutions, a bound from below on the total mass, and a tightness estimate which ensures that no mass is transported to infinity in finite time.
| [1] |
Paolo Perfetti. A Nekhoroshev theorem for some infinite--dimensional systems. Communications on Pure & Applied Analysis, 2006, 5 (1) : 125-146. doi: 10.3934/cpaa.2006.5.125 |
| [2] |
Mustapha Yebdri. Existence of $ \mathcal{D}- $pullback attractor for an infinite dimensional dynamical system. Discrete & Continuous Dynamical Systems - B, 2022, 27 (1) : 167-198. doi: 10.3934/dcdsb.2021036 |
| [3] |
Maciek D. Korzec, Hao Wu. Analysis and simulation for an isotropic phase-field model describing grain growth. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2227-2246. doi: 10.3934/dcdsb.2014.19.2227 |
| [4] |
Mikhail I. Belishev, Sergey A. Simonov. A canonical model of the one-dimensional dynamical Dirac system with boundary control. Evolution Equations & Control Theory, 2022, 11 (1) : 283-300. doi: 10.3934/eect.2021003 |
| [5] |
Ken Shirakawa, Hiroshi Watanabe. Energy-dissipative solution to a one-dimensional phase field model of grain boundary motion. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 139-159. doi: 10.3934/dcdss.2014.7.139 |
| [6] |
Shin-Ichiro Ei, Hirofumi Izuhara, Masayasu Mimura. Infinite dimensional relaxation oscillation in aggregation-growth systems. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1859-1887. doi: 10.3934/dcdsb.2012.17.1859 |
| [7] |
Sergey A. Denisov. Infinite superlinear growth of the gradient for the two-dimensional Euler equation. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 755-764. doi: 10.3934/dcds.2009.23.755 |
| [8] |
Xavier Cabré, Amadeu Delshams, Marian Gidea, Chongchun Zeng. Preface of Llavefest: A broad perspective on finite and infinite dimensional dynamical systems. Discrete & Continuous Dynamical Systems, 2018, 38 (12) : i-iii. doi: 10.3934/dcds.201812i |
| [9] |
María J. Garrido-Atienza, Oleksiy V. Kapustyan, José Valero. Preface to the special issue "Finite and infinite dimensional multivalued dynamical systems". Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : i-iv. doi: 10.3934/dcdsb.201705i |
| [10] |
Kening Lu, Alexandra Neamţu, Björn Schmalfuss. On the Oseledets-splitting for infinite-dimensional random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1219-1242. doi: 10.3934/dcdsb.2018149 |
| [11] |
Sergey V Lototsky, Henry Schellhorn, Ran Zhao. An infinite-dimensional model of liquidity in financial markets. Probability, Uncertainty and Quantitative Risk, 2021, 6 (2) : 117-138. doi: 10.3934/puqr.2021006 |
| [12] |
Pierre Degond, Simone Goettlich, Axel Klar, Mohammed Seaid, Andreas Unterreiter. Derivation of a kinetic model from a stochastic particle system. Kinetic & Related Models, 2008, 1 (4) : 557-572. doi: 10.3934/krm.2008.1.557 |
| [13] |
Akio Ito, Nobuyuki Kenmochi, Noriaki Yamazaki. Global solvability of a model for grain boundary motion with constraint. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 127-146. doi: 10.3934/dcdss.2012.5.127 |
| [14] |
Charles Nguyen, Stephen Pankavich. A one-dimensional kinetic model of plasma dynamics with a transport field. Evolution Equations & Control Theory, 2014, 3 (4) : 681-698. doi: 10.3934/eect.2014.3.681 |
| [15] |
Tomás Caraballo, David Cheban. On the structure of the global attractor for infinite-dimensional non-autonomous dynamical systems with weak convergence. Communications on Pure & Applied Analysis, 2013, 12 (1) : 281-302. doi: 10.3934/cpaa.2013.12.281 |
| [16] |
Markus Böhm, Björn Schmalfuss. Bounds on the Hausdorff dimension of random attractors for infinite-dimensional random dynamical systems on fractals. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3115-3138. doi: 10.3934/dcdsb.2018303 |
| [17] |
J. C. Robinson. A topological time-delay embedding theorem for infinite-dimensional cocycle dynamical systems. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 731-741. doi: 10.3934/dcdsb.2008.9.731 |
| [18] |
Fang-Di Dong, Wan-Tong Li, Li Zhang. Entire solutions in a two-dimensional nonlocal lattice dynamical system. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2517-2545. doi: 10.3934/cpaa.2018120 |
| [19] |
Jong-Shenq Guo, Chang-Hong Wu. Front propagation for a two-dimensional periodic monostable lattice dynamical system. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 197-223. doi: 10.3934/dcds.2010.26.197 |
| [20] |
Tibye Saumtally, Jean-Patrick Lebacque, Habib Haj-Salem. A dynamical two-dimensional traffic model in an anisotropic network. Networks & Heterogeneous Media, 2013, 8 (3) : 663-684. doi: 10.3934/nhm.2013.8.663 |
2020 Impact Factor: 1.432
Tools
Metrics
Other articles
by authors
[Back to Top]