- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 372726, 11 pages
Hyperbolic Relaxation of a Fourth Order Evolution Equation
Departamento de Matemáticas, Pontificia Universidad Javeriana, Cra. 7 No. 43-82, Bogotá, Colombia
Received 26 November 2012; Revised 30 January 2013; Accepted 3 February 2013
Academic Editor: Juan J. Nieto
Copyright © 2013 Renato Colucci and Gerardo R. Chacón. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. Bellettini, G. Fusco, and N. Guglielmi, “A concept of solution and numerical experiments for forward-backward diffusion equations,” Discrete and Continuous Dynamical Systems. Series A, vol. 16, no. 4, pp. 783–842, 2006.
- S. Müller, “Variational models for microstructure and phase transitions,” in Calculus of Variations and Geometric Evolution Problems (Cetraro, 1996), vol. 1713 of Lecture Notes in Mathematics, pp. 85–210, Springer, Berlin, Germany, 1999.
- R. Colucci and G. R. Chacón, “Asymptotic behavior of a fourth order evolution equation,” Submitted paper.
- R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol. 68 of Applied Mathematical Sciences, Springer, New York, NY, USA, 2nd edition, 1997.
- R. Colucci and G. R. Chacón, “Dimension estimate for the global attractor of an evolution equation,” Abstract and Applied Analysis, vol. 2012, Article ID 541426, 18 pages, 2012.
- P. Constantin, C. Foias, B. Nicolaenko, and R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, vol. 70 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1st edition, 1988.
- J. C. Robinson, Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, Mass, USA, 2001.
- P. Galenko, “Phase field model with relaxation of the diffusion flux in non equilibrium solidification of a binary system,” Physiscs Letters A, vol. 287, pp. 190–197, 2001.
- S. Gatti, M. Grasselli, A. Miranville, and V. Pata, “On the hyperbolic relaxation of the one-dimensional Cahn-Hilliard equation,” Journal of Mathematical Analysis and Applications, vol. 312, no. 1, pp. 230–247, 2005.
- S. Zheng and A. Milani, “Global attractors for singular perturbations of the Cahn-Hilliard equations,” Journal of Differential Equations, vol. 209, no. 1, pp. 101–139, 2005.
- A. Segatti, “On the hyperbolic relaxation of the Cahn-Hilliard equation in 3D: approximation and long time behaviour,” Mathematical Models & Methods in Applied Sciences, vol. 17, no. 3, pp. 411–437, 2007.
- M. Grasselli, G. Schimperna, A. Segatti, and S. Zelik, “On the 3D Cahn-Hilliard equation with inertial term,” Journal of Evolution Equations, vol. 9, no. 2, pp. 371–404, 2009.
- H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, NY, USA, 2011.
- J. K. Hale, Asymptotic Behavior of Dissipative Systems, vol. 25 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1988.
- S. Gatti and V. Pata, “A one-dimensional wave equation with nonlinear damping,” Glasgow Mathematical Journal, vol. 48, no. 3, pp. 419–430, 2006.