November  2006, 15(4): 1155-1168. doi: 10.3934/dcds.2006.15.1155

On two-phase Stefan problem arising from a microwave heating process

1. 

Department of Mathematics, Washington State University, Pullman, WA 99164, United States, United States

2. 

Department of Mathematics, Oregon State University, Corvallis, OR 97331, United States

Received  September 2004 Revised  February 2005 Published  May 2006

In this paper we study a free boundary problem modeling a phase-change process by using microwave heating. The mathematical model consists of Maxwell's equations coupled with nonlinear heat conduction with a phase-change. The enthalpy form is used to characterize the phase-change process in the model. It is shown that the problem has a global solution.
Citation: V. S. Manoranjan, Hong-Ming Yin, R. Showalter. On two-phase Stefan problem arising from a microwave heating process. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1155-1168. doi: 10.3934/dcds.2006.15.1155
[1]

Pierluigi Colli, Luca Scarpa. Existence of solutions for a model of microwave heating. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3011-3034. doi: 10.3934/dcds.2016.36.3011

[2]

Yumei Liao, Wei Wei, Xianbing Luo. Existence of solution of a microwave heating model and associated optimal frequency control problems. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2103-2116. doi: 10.3934/jimo.2019045

[3]

A. Jiménez-Casas. Invariant regions and global existence for a phase field model. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 273-281. doi: 10.3934/dcdss.2008.1.273

[4]

José Luiz Boldrini, Gabriela Planas. A tridimensional phase-field model with convection for phase change of an alloy. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 429-450. doi: 10.3934/dcds.2005.13.429

[5]

Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi. Global existence for a two-phase flow model with cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 957-979. doi: 10.3934/dcdsb.2019198

[6]

Manoj Atolia, Prakash Loungani, Helmut Maurer, Willi Semmler. Optimal control of a global model of climate change with adaptation and mitigation. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022009

[7]

Elena Bonetti, Elisabetta Rocca. Global existence and long-time behaviour for a singular integro-differential phase-field system. Communications on Pure and Applied Analysis, 2007, 6 (2) : 367-387. doi: 10.3934/cpaa.2007.6.367

[8]

Emanuela Caliceti, Sandro Graffi. An existence criterion for the $\mathcal{PT}$-symmetric phase transition. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 1955-1967. doi: 10.3934/dcdsb.2014.19.1955

[9]

Mei-Qin Zhan. Global attractors for phase-lock equations in superconductivity. Discrete and Continuous Dynamical Systems - B, 2002, 2 (2) : 243-256. doi: 10.3934/dcdsb.2002.2.243

[10]

Graeme Wake, Anthony Pleasants, Alan Beedle, Peter Gluckman. A model for phenotype change in a stochastic framework. Mathematical Biosciences & Engineering, 2010, 7 (3) : 719-728. doi: 10.3934/mbe.2010.7.719

[11]

Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin. A mathematical model of weight change with adaptation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 873-887. doi: 10.3934/mbe.2009.6.873

[12]

Helmut Abels, Johannes Kampmann. Existence of weak solutions for a sharp interface model for phase separation on biological membranes. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 331-351. doi: 10.3934/dcdss.2020325

[13]

Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model. Networks and Heterogeneous Media, 2017, 12 (2) : 259-275. doi: 10.3934/nhm.2017011

[14]

Kousuke Kuto, Tohru Tsujikawa. Stationary patterns for an adsorbate-induced phase transition model I: Existence. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1105-1117. doi: 10.3934/dcdsb.2010.14.1105

[15]

Marco Campo, Maria I. M. Copetti, José R. Fernández, Ramón Quintanilla. On existence and numerical approximation in phase-lag thermoelasticity with two temperatures. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2221-2245. doi: 10.3934/dcdsb.2021130

[16]

Yasuhito Miyamoto. Global bifurcation and stable two-phase separation for a phase field model in a disk. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 791-806. doi: 10.3934/dcds.2011.30.791

[17]

Hebai Chen, Xingwu Chen, Jianhua Xie. Global phase portrait of a degenerate Bogdanov-Takens system with symmetry. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1273-1293. doi: 10.3934/dcdsb.2017062

[18]

Jackson Itikawa, Jaume Llibre. Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 121-131. doi: 10.3934/dcdsb.2016.21.121

[19]

Antonio Garijo, Armengol Gasull, Xavier Jarque. Local and global phase portrait of equation $\dot z=f(z)$. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 309-329. doi: 10.3934/dcds.2007.17.309

[20]

Hebai Chen, Xingwu Chen. Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ). Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4141-4170. doi: 10.3934/dcdsb.2018130

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (70)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]