Results 201 to 210 of about 9,189,330 (242)
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1993
Abstract The equations derived thus far combine to form an important free-boundary problem for the temperature. The differential equation to be satisfied in bulk is balance of energy supplemented by the constitutive equations (cf. (14.27)): [eq]The evolving interface forms a free boundary, and the corresponding free-boundary conditions ...
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Abstract The equations derived thus far combine to form an important free-boundary problem for the temperature. The differential equation to be satisfied in bulk is balance of energy supplemented by the constitutive equations (cf. (14.27)): [eq]The evolving interface forms a free boundary, and the corresponding free-boundary conditions ...
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On One Nonlocal Problem with Free Boundary
Ukrainian Mathematical Journal, 2001The author considers the equation \( \frac{\partial^2 u}{\partial x^2} + \frac{n-1}{x} \frac{\partial u}{\partial x} - g(u) \frac{\partial u} {\partial t}=0\), \(x,t\in{\mathbb R}_+^1\), \(n=1,2,3.\) The function \( g(u)\), \(u>0\) is positive, continuous, decreasing and has integrable singularity at the point \(u=0.\) By means of the functional \( f(u)
Mitropol'skij, Yu. A. +2 more
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Free Boundary Problems in Solidification of Alloys
SIAM Journal on Mathematical Analysis, 1980Multidimensional three-phase free boundary problems for semilinear diffusion equations are studied as models for the solidification (or melting) of alloys. The intermediate phase represents the “mushy zone” in which the freezing of the remaining liquid provides a heat generation effect.
Alexiades, Vasilios, Cannon, John R.
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A Parabolic-Hyperbolic Free Boundary Problem
SIAM Journal on Mathematical Analysis, 1986The paper is concerned with a parabolic-hyperbolic free boundary problem for change of phase processes in which the melting temperature is space- dependent. A weak formulation is given, pointing out that relevant differences occur with respect to the case of melting temperature. For the case in which weak solutions are suitably smooth it is established
FASANO, ANTONIO, A. FASANO
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2019
One-dimensional Shape Memory Alloy Problem with Duhem Type of Hysteresis Operator.- Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions.- Finite Time Localized Solutions of Fluid Problems with Anisotropic Dissipation.- Parabolic Equations with Anisotropic Nonstandard Growth Conditions ...
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One-dimensional Shape Memory Alloy Problem with Duhem Type of Hysteresis Operator.- Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions.- Finite Time Localized Solutions of Fluid Problems with Anisotropic Dissipation.- Parabolic Equations with Anisotropic Nonstandard Growth Conditions ...
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Boundary regularity for free boundary problems
Communications on Pure and Applied Mathematics, 1999The purpose of this paper is to study up-to-the-boundary regularity of solutions of elliptic free boundary problems with two phases. The solution of a typical problem can be described as a function \(u\) that is harmonic in \(\{u\neq 0\}\) and satisfies the gradient jump condition: \(| \nabla u^+|^2 -|\nabla u^-|^2=1\) on the free boundary \(\{u= 0\}\).
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On a Free Boundary Problem, the Starlike Case
SIAM Journal on Mathematical Analysis, 1975Let $\mathcal{D}$ be a doubly connected region limited by the infinite point and a starlike boundary component $\Gamma $ which does not reduce to a point. If $\lambda $ is a given positive number, we show there exists a unique annulus $\omega _\lambda \subset \mathcal{D}$ having $\Gamma $ as one boundary component and another boundary component $\gamma
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Time Dependent Free Boundary Problems
SIAM Review, 1979Recent results on the existence and continuity of solutions, and on the shape and smoothness of the free boundary are described for the following problems: (a) the flow of liquid in a dam with time...
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1994
The study of the free boundary problems was started working in China as early as 1960 ([14] [19]). Since then many mathematicians have been concentrating their effects to the theoretical researches on phase change problems, filtration problems, etc.
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The study of the free boundary problems was started working in China as early as 1960 ([14] [19]). Since then many mathematicians have been concentrating their effects to the theoretical researches on phase change problems, filtration problems, etc.
openaire +1 more source