American Institute of Mathematical Sciences

Advanced
2007, 2007(Special): 741-750. doi: 10.3934/proc.2007.2007.741

Limit of kinetic term for a Stefan problem

Piotr B. Mucha 1,

1. 

Warsaw University, Inst. of Applied Math. and Mech., ul. Banacha 2, 02-097 Warszawa, Poland

Received  September 2006 Revised  April 2007 Published  September 2007

We investigate solutions to the one-phase quasi-stationary Stefan problem with the surface tension and kinetic term. Main results show existence of unique regular solutions with a suitable bound which enables to obtain the limit as the kinetic term is vanishing. Our problem is considered in anisotropic Besov spaces locally in time.
Keywords: nonlocal parabolic systems, curvature, optimal regularity., Besov spaces, Stefan problems, vanishing kinetic effects.
Mathematics Subject Classification: Primary: 35R35, 35K5.
Citation: 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
[1]

Irene Benedetti, Luisa Malaguti, Valentina Taddei. Nonlocal problems in Hilbert spaces. Conference Publications, 2015, 2015 (special) : 103-111. doi: 10.3934/proc.2015.0103
[2]

Mikil Foss, Joe Geisbauer. Higher differentiability in the context of Besov spaces for a class of nonlocal functionals. Evolution Equations & Control Theory, 2013, 2 (2) : 301-318. doi: 10.3934/eect.2013.2.301
[3]

Abdelkader Boucherif. Nonlocal problems for parabolic inclusions. Conference Publications, 2009, 2009 (Special) : 82-91. doi: 10.3934/proc.2009.2009.82
[4]

Daoyuan Fang, Chenyin Qian. Regularity criterion for 3D Navier-Stokes equations in Besov spaces. Communications on Pure & Applied Analysis, 2014, 13 (2) : 585-603. doi: 10.3934/cpaa.2014.13.585
[5]

Minghua Yang, Jinyi Sun. Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1617-1639. doi: 10.3934/cpaa.2017078
[6]

Monica Motta, Caterina Sartori. Asymptotic problems in optimal control with a vanishing Lagrangian and unbounded data. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4527-4552. doi: 10.3934/dcds.2015.35.4527
[7]

Fengping Yao. Optimal regularity for parabolic Schrödinger operators. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1407-1414. doi: 10.3934/cpaa.2013.12.1407
[8]

Gary Lieberman. Nonlocal problems for quasilinear parabolic equations in divergence form. Conference Publications, 2003, 2003 (Special) : 563-570. doi: 10.3934/proc.2003.2003.563
[9]

Yushi Nakano, Shota Sakamoto. Spectra of expanding maps on Besov spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1779-1797. doi: 10.3934/dcds.2019077
[10]

Alberto Fiorenza, Anna Mercaldo, Jean Michel Rakotoson. Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 893-906. doi: 10.3934/dcds.2002.8.893
[11]

Sunra J. N. Mosconi. Optimal elliptic regularity: A comparison between local and nonlocal equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (3) : 547-559. doi: 10.3934/dcdss.2018030
[12]

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
[13]

Irene Benedetti, Nguyen Van Loi, Valentina Taddei. An approximation solvability method for nonlocal semilinear differential problems in Banach spaces. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 2977-2998. doi: 10.3934/dcds.2017128
[14]

Shuhong Chen, Zhong Tan. Optimal interior partial regularity for nonlinear elliptic systems. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 981-993. doi: 10.3934/dcds.2010.27.981
[15]

Pierre Degond, Hailiang Liu. Kinetic models for polymers with inertial effects. Networks & Heterogeneous Media, 2009, 4 (4) : 625-647. doi: 10.3934/nhm.2009.4.625
[16]

Masoumeh Dashti, Stephen Harris, Andrew Stuart. Besov priors for Bayesian inverse problems. Inverse Problems & Imaging, 2012, 6 (2) : 183-200. doi: 10.3934/ipi.2012.6.183
[17]

Baoxiang Wang. E-Besov spaces and dissipative equations. Communications on Pure & Applied Analysis, 2004, 3 (4) : 883-919. doi: 10.3934/cpaa.2004.3.883
[18]

Hermann Brunner, Jingtang Ma. Abstract cascading multigrid preconditioners in Besov spaces. Communications on Pure & Applied Analysis, 2006, 5 (2) : 349-365. doi: 10.3934/cpaa.2006.5.349
[19]

Jin-Mun Jeong, Seong-Ho Cho. Identification problems of retarded differential systems in Hilbert spaces. Evolution Equations & Control Theory, 2017, 6 (1) : 77-91. doi: 10.3934/eect.2017005
[20]

Luisa Fattorusso, Antonio Tarsia. Regularity in Campanato spaces for solutions of fully nonlinear elliptic systems. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1307-1323. doi: 10.3934/dcds.2011.31.1307

 Impact Factor: 

Tools

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences