# American Institute of Mathematical Sciences

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 & 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 & 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 & 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 & 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 & 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 & Continuous Dynamical Systems - B, 2020, 25 (3) : 957-979. doi: 10.3934/dcdsb.2019198 [6] Elena Bonetti, Elisabetta Rocca. Global existence and long-time behaviour for a singular integro-differential phase-field system. Communications on Pure & Applied Analysis, 2007, 6 (2) : 367-387. doi: 10.3934/cpaa.2007.6.367 [7] Emanuela Caliceti, Sandro Graffi. An existence criterion for the $\mathcal{PT}$-symmetric phase transition. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1955-1967. doi: 10.3934/dcdsb.2014.19.1955 [8] Mei-Qin Zhan. Global attractors for phase-lock equations in superconductivity. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 243-256. doi: 10.3934/dcdsb.2002.2.243 [9] 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 [10] 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 [11] Helmut Abels, Johannes Kampmann. Existence of weak solutions for a sharp interface model for phase separation on biological membranes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 331-351. doi: 10.3934/dcdss.2020325 [12] Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model. Networks & Heterogeneous Media, 2017, 12 (2) : 259-275. doi: 10.3934/nhm.2017011 [13] Kousuke Kuto, Tohru Tsujikawa. Stationary patterns for an adsorbate-induced phase transition model I: Existence. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1105-1117. doi: 10.3934/dcdsb.2010.14.1105 [14] Marco Campo, Maria I. M. Copetti, José R. Fernández, Ramón Quintanilla. On existence and numerical approximation in phase-lag thermoelasticity with two temperatures. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021130 [15] Yasuhito Miyamoto. Global bifurcation and stable two-phase separation for a phase field model in a disk. Discrete & Continuous Dynamical Systems, 2011, 30 (3) : 791-806. doi: 10.3934/dcds.2011.30.791 [16] Hebai Chen, Xingwu Chen, Jianhua Xie. Global phase portrait of a degenerate Bogdanov-Takens system with symmetry. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1273-1293. doi: 10.3934/dcdsb.2017062 [17] Jackson Itikawa, Jaume Llibre. Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 121-131. doi: 10.3934/dcdsb.2016.21.121 [18] Antonio Garijo, Armengol Gasull, Xavier Jarque. Local and global phase portrait of equation $\dot z=f(z)$. Discrete & Continuous Dynamical Systems, 2007, 17 (2) : 309-329. doi: 10.3934/dcds.2007.17.309 [19] Hebai Chen, Xingwu Chen. Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ). Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4141-4170. doi: 10.3934/dcdsb.2018130 [20] Keisuke Matsuya, Tetsuji Tokihiro. Existence and non-existence of global solutions for a discrete semilinear heat equation. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 209-220. doi: 10.3934/dcds.2011.31.209

2020 Impact Factor: 1.392