Results 221 to 230 of about 64,698 (263)
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Nonlinear Analysis: Theory, Methods & Applications, 2008
We are concerned with the existence of positive solutions of the following discontinuous problem: \[ -\Delta u=f(u)H(u-\mu)\quad\text{in }\Omega, \qquad u=h\quad\text{on }\partial\Omega, \] where \(\Omega\) is the unit ball of \(\mathbb R^n\) \((n\geq 3)\) and \(H\)H is the Heaviside function.
Bensid, Sabri, Bouguima, S. M.
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We are concerned with the existence of positive solutions of the following discontinuous problem: \[ -\Delta u=f(u)H(u-\mu)\quad\text{in }\Omega, \qquad u=h\quad\text{on }\partial\Omega, \] where \(\Omega\) is the unit ball of \(\mathbb R^n\) \((n\geq 3)\) and \(H\)H is the Heaviside function.
Bensid, Sabri, Bouguima, S. M.
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2003
Abstract This chapter is the most unconventional in the book. Whereas hyperbolic, elliptic and parabolic problems have been studied over many decades, and many texts are devoted to each, the subject of free boundary problems has attracted few specialised publications despite its importance in modern applied mathematics.
John Ockendon +3 more
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Abstract This chapter is the most unconventional in the book. Whereas hyperbolic, elliptic and parabolic problems have been studied over many decades, and many texts are devoted to each, the subject of free boundary problems has attracted few specialised publications despite its importance in modern applied mathematics.
John Ockendon +3 more
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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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ON A STEFAN PROBLEM WITH AN EMERGING FREE BOUNDARY
Numerical Heat Transfer, 1981This paper provides a closed-form solution and an optimization approximation to a degenerate Stefan problem. A truncation of the exact solution and the approximation obtained by using the authors' optimization technique yield highly accurate results with strict error bounds in a situation where other techniques are difficult to apply.
C. J. Lozano, R. Reemtsen
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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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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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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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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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A Novel Free Boundary Problem-the Sauna
Journal of Partial Differential Equations, 1989Die Arbeit untersucht ein freies Randwertproblem im Zusammenhang mit einer parabolischen Gleichung mit unstetigen Koeffizienten und einer Inhomogenität, deren Sprung den freien Rand definiert; allerdings ist das System sehr unvollständig definiert und ist ohne eine andere Arbeit [\textit{R. M. Furzeland} and \textit{E. B. Hansen}, IMA J. Appl. Math. 34,
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