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1.
E. V. Frolova 《Journal of Mathematical Sciences》2009,159(4):580-595
The unique solvability of the two-phase Stefan problem with a small parameter ε ∈ [0; ε
0] at the time derivative in the heat equations is proved. The solution is obtained on a certain time interval [0; t
0] independent of ε. The solution of the Stefan problem is compared with the solution to the Hele–Shaw problem corresponding to the case ε = 0. The solutions of both problems are not assumed to coincide at the initial moment of time. Bibliography: 18 titles.
Dedicated to Vsevolod Alekseevich Solonnikov on the occasion of his jubilee
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 337–363. 相似文献
2.
A theorem on differential inequalities related to a simple parabolic free boundary value problem is presented. The result can be used for the construction of pointwise upper and lower bounds of the free boundary curve. 相似文献
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This paper considers the time dependent stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries: The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments. 相似文献
4.
I. I. Danilyuk 《Journal of Mathematical Sciences》1983,21(3):268-273
An approximative method for solving the quasistationary thermophysical Stefan problem is presented. 相似文献
5.
Summary
Existence and unicity for the solution of the one-dimensional two-phase Stefan problem with energy specification
in the liquid phase is established via potential theoretic arguments employing the Schauder fixed point theorem and a contracting map.This work was supported in part by NSF Grant MCS-7801687.This work was carried out at UT-Austin while on sabbatical from the University of Adelaide. 相似文献
6.
E. N. Solov'eva 《Computational Mathematics and Modeling》1990,1(1):18-22
An iterative process is constructed for numerical solution of weakly stable boundary-value problems for parabolic equations with unknown moving boundaries. Special emphasis is placed on the choice of the initial approximation.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 37–43, 1985. 相似文献
7.
The problem with unknown boundaries for a first-order semilinear hyperbolic system is studied in the case where the curve of definition of the initial conditions degenerates to a point. An existence and uniqueness theorem for a classical solution of the problem is proved for small t. 相似文献
8.
We consider the Stefan problem with Dirichlet boundary conditions depending on a hysteresis functional where the free boundary
is involved. We show existence of a positive valueT and existence of aT-periodic solution of the problem, provided the Stefan number is sufficiently small and the hysteresis functional is described
by the elementary rectangular hysteresis loop. If in addition the Preisach hysteresis operator is Lipschitz-continuous we
prove that every periodic solution must be stationary.
Dedicated to Professor Avner Friedman on occasion of his 60th birthday
supported by Humboldt Foundation Scholarship 相似文献
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Using the method of contracting mappings, we prove, for small values of time, the existence and uniqueness of a generalized
Lipschitz solution of a mixed problem with unknown boundaries for a hyperbolic quasilinear system of first-order equations
represented in terms of Riemann invariants with nonlocal (nonseparated and integral) boundary conditions. 相似文献
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Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound ‖u(t, ·) ? u?(t, ·)‖ = O(1)(1 + t) · |ln ?| on the distance between an exact BV solution u and a viscous approximation u?, letting the viscosity coefficient ? → 0. In the proof, starting from u we construct an approximation of the viscous solution u? by taking a mollification u * and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed ?. Error estimates are then obtained by introducing new Lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families. © 2004 Wiley Periodicals, Inc. 相似文献
14.
We investigate partially ordered normed vector spaces in which the norm convergence coincides with the order convergence. We consider spaces where the convergences coincide for arbitrary nets and spaces where the convergences coincide only for sequences. We give conditions which characterize such spaces and investigate their properties. In particular, we study the problem of their Dedekind completeness and -completeness.Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 259–268, February, 1973. 相似文献
15.
Andreea C. Nicoara 《Mathematische Annalen》2012,354(4):1223-1245
On a smooth domain in ${{\mathbb {C}}^n}$ of finite D’Angelo q-type at a point, an effective upper bound for the vanishing order of the Levi determinant ${{\rm coeff}\{\partial r \wedge {\bar \partial} r \wedge (\partial {\bar \partial} r)^{n-q}\}}$ at that point is given in terms of the D’Angelo q-type, the dimension of the space n, and q itself. The argument uses Catlin’s notion of a boundary system as well as techniques pioneered by John D’Angelo. 相似文献
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Prof. Dr. K.-H. Hoffmann Prof. Dr. J. Sprekels 《Numerical Functional Analysis & Optimization》2013,34(1):47-76
A two-phase Stefan-problem is considered where the progress of the free boundary is observed by fully automatic real-time controls (thermostats or photo-electric cells). The heat flux at both fixed boundaries can be determined by heaters which respond to the signals of the controls, possibly with a certain time lag. The corresponding mathematical model leads to a two-phase Stefan problem with nonlinear and discontinuous boundary conditions with delays at the fixed boundaries. The problem is transformed into a set-valued fixed point equation, and the existence of a solution is shown with the aid of a theorem due to Bohnenblust-Karlin. The consequence of this result is that a free boundary with the well-known smoothness properties develops under the impact of a fully automatic real-time control via thermostats or photo-electric cells. Some numerical experiments conclude the paper. They indicate that the model is realistic. 相似文献
19.
Irena Pawlow Yuji Shindo Yoshiyuki Sakawa 《Numerical Functional Analysis & Optimization》2013,34(1-2):55-82
This paper treats a multidimensional two-phase Stefan problem with variable coefficients and mixed type boundary conditions. A numerical method for solving the problem is of fixed domain type, based on a variational inequality formulation of the problem. Numerical solutions are obtained by using piecewise linear finite elements in space and finite difference in time, and by solving a strictly convex minimization problem at each time step. Some computational results are presented. 相似文献
20.
The problem presented below is a singular-limit problem of the extension of the Cahn-Hilliard model obtained via introducing the asymmetry of the surface tension tensor under one of the truncations (approximations) of the inner energy [2, 5–8, 10, 12, 13]. 相似文献