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A result on singularly perturbed elliptic problems
On the pointwise jump condition at the free boundary in the 1-phase Stefan problem
1. | Department of Mathematics, Purdue University, United States |
2. | Department of Mathematics, Kansas State University, Manhattan, KS 66506, United States |
[1] |
Luigi Ambrosio, Michele Miranda jr., Diego Pallara. Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 591-606. doi: 10.3934/dcds.2010.28.591 |
[2] |
Alessandro Ferriero, Nicola Fusco. A note on the convex hull of sets of finite perimeter in the plane. Discrete and Continuous Dynamical Systems - B, 2009, 11 (1) : 103-108. doi: 10.3934/dcdsb.2009.11.103 |
[3] |
Chaoxu Pei, Mark Sussman, M. Yousuff Hussaini. A space-time discontinuous Galerkin spectral element method for the Stefan problem. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 3595-3622. doi: 10.3934/dcdsb.2017216 |
[4] |
Chifaa Ghanmi, Saloua Mani Aouadi, Faouzi Triki. Recovering the initial condition in the one-phase Stefan problem. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1143-1164. doi: 10.3934/dcdss.2021087 |
[5] |
Fanghua Lin, Dan Liu. On the Betti numbers of level sets of solutions to elliptic equations. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4517-4529. doi: 10.3934/dcds.2016.36.4517 |
[6] |
Marianne Korten, Charles N. Moore. Regularity for solutions of the two-phase Stefan problem. Communications on Pure and Applied Analysis, 2008, 7 (3) : 591-600. doi: 10.3934/cpaa.2008.7.591 |
[7] |
Michael L. Frankel, Victor Roytburd. A Finite-dimensional attractor for a nonequilibrium Stefan problem with heat losses. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 35-62. doi: 10.3934/dcds.2005.13.35 |
[8] |
Adriana C. Briozzo, María F. Natale, Domingo A. Tarzia. The Stefan problem with temperature-dependent thermal conductivity and a convective term with a convective condition at the fixed face. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1209-1220. doi: 10.3934/cpaa.2010.9.1209 |
[9] |
Qingjie Hu, Zhihao Ge, Yinnian He. Discontinuous Galerkin method for the Helmholtz transmission problem in two-level homogeneous media. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 2923-2948. doi: 10.3934/dcdsb.2020046 |
[10] |
Mario Roldan. Hyperbolic sets and entropy at the homological level. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3417-3433. doi: 10.3934/dcds.2016.36.3417 |
[11] |
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 |
[12] |
Lincoln Chayes, Inwon C. Kim. The supercooled Stefan problem in one dimension. Communications on Pure and Applied Analysis, 2012, 11 (2) : 845-859. doi: 10.3934/cpaa.2012.11.845 |
[13] |
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 |
[14] |
Marvin S. Müller. Approximation of the interface condition for stochastic Stefan-type problems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4317-4339. doi: 10.3934/dcdsb.2019121 |
[15] |
Jan Prüss, Jürgen Saal, Gieri Simonett. Singular limits for the two-phase Stefan problem. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5379-5405. doi: 10.3934/dcds.2013.33.5379 |
[16] |
Karl P. Hadeler. Stefan problem, traveling fronts, and epidemic spread. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 417-436. doi: 10.3934/dcdsb.2016.21.417 |
[17] |
Gyula Csató. On the isoperimetric problem with perimeter density $r^p$. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2729-2749. doi: 10.3934/cpaa.2018129 |
[18] |
Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1431-1443. doi: 10.3934/cpaa.2013.12.1431 |
[19] |
Everaldo S. de Medeiros, Jianfu Yang. Asymptotic behavior of solutions to a perturbed p-Laplacian problem with Neumann condition. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 595-606. doi: 10.3934/dcds.2005.12.595 |
[20] |
Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615 |
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