This chapter presents an investigation of a one-phase Stefan problem by means of the Legendre transform. Applying the Legendre transform to a free boundary value problem forgives rise to a new problem with a smooth free boundary but with a highly nonlinear equation, even in the simplest case....
We study the existence and properties of solutions and free boundaries of the one-phase Stefan problem with fractional diffusion posed in N . In terms of the enthalpy h ( x , t ) , the evolution equation reads t h + ( Δ ) s Φ ( h ) = 0 , while the temperature is defined as...
In the present paper, we consider the multi-dimensional one-phase Stefan problem describing the process of phase transition in an incompressible viscous fluid. The model is described as a free boundary problem consisting of the heat equation with a transport term and the Navier–Stokes equations. ...
Feedback controllability of the free boundary of the one phase Stefan problem In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varyi... Viorel,Barbu,Giuseppe,... - 《Differential & Integral...
Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary We consider a one-phase Stefan problem for the heat equation with a nonlinear reaction term. We first exhibit an energy condition, involving the initial da... H Ghidouche,SD Tarzia - 《...
Three exponential iterative methods for one-dimensional one-phase Stefan problems based on the transformation of the moving boundary problem into a mixed one, the discretization of the time variable, and the piecewise linearization of the resulting two-point boundary-value problem at each time step ...
The one phase stochastic Stefan problem with random disturbance is expressed by using the stochastic variational inequality. The key idea in studying the existence and uniqueness properties of the solution of a stochastic variational inequality is the introduction of the theory of non-linear stochastic ...
The one-phase Stefan problem was simulated numerically in a layer of semitransparent medium with different emissivity factors at the right moving boundary... NA Rubtsov,SD Sleptsov - 《Thermophysics & Aeromechanics》 被引量: 5发表: 2010年 Antireflection coating on a surface with high reflecting pow...
Well-posedness of one-phase Stefan problems for sublinear heat equations Aiki, T., Imai, H., Ishimura, N., Yamada, Y.: Well-posedness of one-phase Stefan problems for sublinear heat equations. Nonlinear Anal. Ser. A:... Toyohiko,Aiki,and,... - 《Nonlinear Analysis》 被引量: 10发表:...
A one-dimensional Stefan problem involving several phases (solid, liquid, vapor) which can appear and disappear is considered. A numerical method for such problems is described and numerically tested. It is derived from a previous method of the same authors for one-phase problems. It is a ...