American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 281-287. doi: 10.3934/proc.2003.2003.281

Fractal dimension of attractors for a Stefan problem

Michael L. Frankel 1, and  Victor Roytburd 2,

1. 

Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN 46202-3216, United States
2. 

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590

Received  August 2002 Revised  March 2003 Published  April 2003

For a one-phase free-boundary problem with kinetics, which is known to generate a rich dynamics, we present results of a numerical study of the correlation dimension of the attractor.
Keywords: Stefan problem, correlation dimension., Free boundaries.
Mathematics Subject Classification: Primary: 35R35, 80A25; Secondary 35K5.
Citation: Michael L. Frankel, Victor Roytburd. Fractal dimension of attractors for a Stefan problem. Conference Publications, 2003, 2003 (Special) : 281-287. doi: 10.3934/proc.2003.2003.281
[1]

Lincoln Chayes, Inwon C. Kim. The supercooled Stefan problem in one dimension. Communications on Pure & Applied Analysis, 2012, 11 (2) : 845-859. doi: 10.3934/cpaa.2012.11.845
[2]

Chonghu Guan, Xun Li, Zuo Quan Xu, Fahuai Yi. A stochastic control problem and related free boundaries in finance. Mathematical Control & Related Fields, 2017, 7 (4) : 563-584. doi: 10.3934/mcrf.2017021
[3]

Donatella Danielli, Marianne Korten. On the pointwise jump condition at the free boundary in the 1-phase Stefan problem. Communications on Pure & Applied Analysis, 2005, 4 (2) : 357-366. doi: 10.3934/cpaa.2005.4.357
[4]

David Jerison, Nikola Kamburov. Free boundaries subject to topological constraints. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 7213-7248. doi: 10.3934/dcds.2019301
[5]

Piotr B. Mucha. Limit of kinetic term for a Stefan problem. Conference Publications, 2007, 2007 (Special) : 741-750. doi: 10.3934/proc.2007.2007.741
[6]

Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817
[7]

Antonio Fasano, Mario Primicerio, Andrea Tesi. A mathematical model for spaghetti cooking with free boundaries. Networks & Heterogeneous Media, 2011, 6 (1) : 37-60. doi: 10.3934/nhm.2011.6.37
[8]

Marcelo Disconzi. On a linear problem arising in dynamic boundaries. Evolution Equations & Control Theory, 2014, 3 (4) : 627-644. doi: 10.3934/eect.2014.3.627
[9]

Jan Prüss, Jürgen Saal, Gieri Simonett. Singular limits for the two-phase Stefan problem. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5379-5405. doi: 10.3934/dcds.2013.33.5379
[10]

Marianne Korten, Charles N. Moore. Regularity for solutions of the two-phase Stefan problem. Communications on Pure & Applied Analysis, 2008, 7 (3) : 591-600. doi: 10.3934/cpaa.2008.7.591
[11]

Karl P. Hadeler. Stefan problem, traveling fronts, and epidemic spread. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 417-436. doi: 10.3934/dcdsb.2016.21.417
[12]

Xin-Guo Liu, Kun Wang. A multigrid method for the maximal correlation problem. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 785-796. doi: 10.3934/naco.2012.2.785
[13]

Mingxin Wang, Qianying Zhang. Dynamics for the diffusive Leslie-Gower model with double free boundaries. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2591-2607. doi: 10.3934/dcds.2018109
[14]

Yuan Wu, Jin Liang. Free boundaries of credit rating migration in switching macro regions. Mathematical Control & Related Fields, 2019, 0 (0) : 0-0. doi: 10.3934/mcrf.2019038
[15]

Meng Zhao, Wan-Tong Li, Wenjie Ni. Spreading speed of a degenerate and cooperative epidemic model with free boundaries. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 981-999. doi: 10.3934/dcdsb.2019199
[16]

V. S. Manoranjan, Hong-Ming Yin, R. Showalter. On two-phase Stefan problem arising from a microwave heating process. Discrete & Continuous Dynamical Systems - A, 2006, 15 (4) : 1155-1168. doi: 10.3934/dcds.2006.15.1155
[17]

Michael L. Frankel, Victor Roytburd. A Finite-dimensional attractor for a nonequilibrium Stefan problem with heat losses. Discrete & Continuous Dynamical Systems - A, 2005, 13 (1) : 35-62. doi: 10.3934/dcds.2005.13.35
[18]

Claude-Michel Brauner, Josephus Hulshof, Luca Lorenzi. Stability of the travelling wave in a 2D weakly nonlinear Stefan problem. Kinetic & Related Models, 2009, 2 (1) : 109-134. doi: 10.3934/krm.2009.2.109
[19]

Chaoxu Pei, Mark Sussman, M. Yousuff Hussaini. A space-time discontinuous Galerkin spectral element method for the Stefan problem. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3595-3622. doi: 10.3934/dcdsb.2017216
[20]

Huiling Li, Xiaoliu Wang, Xueyan Lu. A nonlinear Stefan problem with variable exponent and different moving parameters. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1671-1698. doi: 10.3934/dcdsb.2019246

 Impact Factor: 

Tools

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences