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Uniqueness of moving boundary for a heat conduction problem with nonlinear interface conditions

T. Wei
2010 Applied Mathematics Letters  
In this paper, based on the maximum principle and the unique continuation theorem, we present a uniqueness result for a moving boundary of a heat problem in a multilayer medium with nonlinear interface  ...  conditions.  ...  The formulation of a boundary identification problem with nonlinear interface conditions In this paper, we consider a heat conduction problem in a multilayer domain with a moving boundary s(t).  ... 
doi:10.1016/j.aml.2010.01.018 fatcat:druqevgs4fe23g5h3xwwpzequa

Input-to-State Stability for the Control of Stefan Problem with Respect to Heat Loss [article]

Shumon Koga, Iasson Karafyllis, Miroslav Krstic
2019 arXiv   pre-print
First, we introduce the one-phase Stefan problem with a heat loss at the interface by modeling the dynamics of the liquid temperature and the interface position.  ...  The similar manner is employed to the two-phase Stefan problem with the heat loss at the boundary of the solid phase under the control law proposed in [25], from which we deduce an analogous result for  ...  A nonlinear backstepping transformation for moving boundary problems is utilized, and the estimate of the L 2 norm is derived in the sense of ISS with respect to the heat loss at the interface.  ... 
arXiv:1903.01447v1 fatcat:pa63gzpf4vhz3o7ftdhnuybndm

Page 6700 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews  
The author considers the supercooled Stefan problem with a general anisotropic curvature- and velocity-dependent boundary condition on the moving interface.  ...  A. On the solution of one-dimensional nonlinear problems of heat conduction on an isothermic grid. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 29 (1989), no. 11, 1742-1746, 1760.  ... 

The Numerical Solution of One-Dimensional Phase Change Problems Using an Adaptive Moving Mesh Method

J.A. Mackenzie, M.L. Robertson
2000 Journal of Computational Physics  
An adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of heat conduction problems with a phase change.  ...  Numerical examples are given for a two-phase freezing problem, a model of a spot-welding process, and a three-phase problem with a varying number of interfaces.  ...  for multi-phase problems with different latent heat jumps.  ... 
doi:10.1006/jcph.2000.6511 fatcat:x3qezmmu2zbntddt5t4e7r36vm

Direct and inverse one-phase Stefan problem solved by the variational iteration method

Damian Słota
2007 Computers and Mathematics with Applications  
The direct problem consists in a calculation of temperature distribution and of a function which describes the position of the moving interface, whilst the inverse problem consists in a calculation of  ...  temperature distribution as well as in the reconstruction of the function which describes the temperature distribution on the boundary, when the position of the moving interface is known.  ...  Acknowledgements The author wishes to thank Professor Ji-Huan He for his suggestions, leading to the present improved version of my paper.  ... 
doi:10.1016/j.camwa.2006.12.061 fatcat:6sapyqn3rzed7mokveskicin6m

Page 8832 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
The problem is reduced to two one-phase moving boundary problems for the linear heat equation, connected through a constraint on the relative motion of their moving boundaries.  ...  2004k:35418 nonlinear heat conduction is considered.  ... 

Page 4495 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
(UKR-AOS-AR; Kiev) Exact solutions of a class of nonlinear boundary value problems with moving boundaries. J. Phys. A 26 (1993), no. 18, L935-L940.  ...  Exact solutions of traveling wave type are constructed for a two- phase Stefan problem for a nonlinear heat equation.  ... 

A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains

Matteo Bonforte, Juan Luis Vázquez
2015 Archive for Rational Mechanics and Analysis  
As L we can take the most common definitions of the fractional Laplacian (−∆) s , 0 < s < 1, in a bounded domain with zero Dirichlet boundary conditions, as well as more general classes of operators.  ...  We also briefly show existence and uniqueness of H −s solutions with a different approach.  ...  Voller, University of Minnesota The Stefan problem, involving the tracking of a phase change interface, provides the framework for studying moving boundary problems in a variety of physical situations.  ... 
doi:10.1007/s00205-015-0861-2 fatcat:cfwell5n7bbaheb5ftt2cg5xyu

A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems

Domingo Alberto Tarzia
2000 MAT Serie A  
cuyo objetivo es contribuir a la difusión de conocimientos y resultados matemáticos.  ...  La serie A y las Prepublicaciones podrán ser consultadas en:  ...  ., "Exact solutions of a class of nonlinear boundary value problems with moving boundaries", J.Phys.A:Math.Gen.HUPPERT H.E.  ... 
doi:10.26422/mat.a.2000.2.tar fatcat:ikpa45typfghzfbj5hhb6dds5q

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

B. Tomas Johansson, Daniel Lesnic, Thomas Reeve
2014 Mathematics and Computers in Simulation  
We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case.  ...  The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface.  ...  Lesnic would like to thank the Isaac Newton Institute for the Visiting Fellowships within the programme on "Inverse Problems" offered in November-December 2011 during which period some of this work has  ... 
doi:10.1016/j.matcom.2014.03.004 fatcat:fpmufuyowbguxgfxml3z7dxwme

Backstepping Control of the One-Phase Stefan Problem [article]

Shumon Koga, Mamadou Diagne, Shuxia Tang, Miroslav Krstic
2016 arXiv   pre-print
A new nonlinear backstepping transformation for moving boundary problem is utilized to transform the original coupled PDE-ODE system into a target system whose exponential stability is proved.  ...  The full-state boundary feedback controller ensures the exponential stability of the moving interface to a reference setpoint and the H_1-norm of the distributed temperature by a choice of the setpint  ...  Well-posedness of a moving boundary problem arising in a dissolution-growth process. ] N. Petit. Control problems for one-dimensional fluids and reactive fluids with moving interfaces.  ... 
arXiv:1607.04345v1 fatcat:gbnw3kokznfu3evzjt2swx6ppu

Page 1977 of Mathematical Reviews Vol. , Issue 93d [page]

1993 Mathematical Reviews  
The convergence of the approximated parameters is proven for a certain class of these moving boundary problems.  ...  Then the distributional generalized heat balance equation is coupled with a suitable PDE for a new unknown function 9, designed so that the level surfaces of g provide the interfaces of the Stefan problem  ... 

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface [chapter]

Domingo Alberto
2011 Advanced Topics in Mass Transfer  
The goal of this chapter is firstly to give a survey of some explicit and approximated solutions for heat and mass transfer problems in which a free or moving interface is involved.  ...  Secondly, we show simultaneously some new recent problems for heat and mass transfer, in which a free or moving interface is also involved. We will consider the following problems: 1.  ...  Acknowledgements This paper was partially sponsored by the project PIP No. 0460 of CONICET -UA (Rosario, Argentina), and Grant FA9550-10-1-0023.  ... 
doi:10.5772/14537 fatcat:thy7kkuq6rg6dfqalm3xvcubfq

Page 2151 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
The free boundary problem that describes the model involves initial and boundary conditions, in- cluding a nonlinear kinetic condition at the interface.  ...  Sci. 30 (1992), no. 5, 657-664; MR 93a:73007], we give uniqueness theorems for initial value and boundary value problems concerning a Cattaneo type rigid or deformable heat conducting bar.  ... 

Page 6722 of Mathematical Reviews Vol. , Issue 93m [page]

1993 Mathematical Reviews  
Summary: “We consider a one-phase Stefan problem with surface tension in dimension two and show a well-posedness result in the neighborhood of a stationary solution, in the case where the moving interface  ...  First the uniqueness, existence and con- tinuous dependence for the direct problem with the fixed electrical conductivity are proved.  ... 
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