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Free boundary problem
About: Free boundary problem is a research topic. Over the lifetime, 15390 publications have been published within this topic receiving 274687 citations.
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Journal Article•
TL;DR: In this paper, a m-point boundary value problem for a Robin second-order differential equation is investigated and the fixed point theorem of Cone expansion-commpression type is used as a sufficient condition for the existence of positive solution.
Abstract: A m-point boundary value problem for a Robin second-order differential equation is investigated;By using fixed point theorem of Cone expansion-commpression type a sufficient condition for the existence of positive solution is obtained.
3 citations
Posted Content•
TL;DR: In this article, the authors considered one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary and obtained a necessary and sufficient condition for infinite differentiability.
Abstract: We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on $C^m$-regularity of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.
3 citations
01 Jul 1992
TL;DR: In this article, the acoustic effects of the surrounding air around a harmonically vibrating solar array in a testroom are estimated using a boundary integral ansatz, which involves the solution of a hypersingular integral equation which is numerically solved by a boundary element method.
Abstract: In this paper the acoustic effects of the surrounding air around a harmonically vibrating solar array in a testroom are estimated. The dynamics of the solar array is modelled by a differential equation for a harmonically vibrating plate and the sound pressure of the vibrating air is modelled by a boundary integral ansatz. The contribution of the sound pressure on the solar array results in a perturbed eigenvalue problem which is approximately solved by perturbation analysis up to first order with respect to the ratio of the density of the air and the density of the solar array. This analysis involves the solution of a hypersingular integral equation which is numerically solved by a boundary element method.
3 citations
01 Sep 2017
TL;DR: The proposed paper is devoted to the information and communication technologies applied in the study of Stefan type free boundaries problems and solutions to one-dimensional free boundary problem are obtained using MatLab matrix-oriented environment.
Abstract: The proposed paper is devoted to the information and communication technologies applied in the study of Stefan type free boundaries problems. Solutions to one-dimensional free boundary problem are obtained using MatLab matrix-oriented environment.
3 citations
TL;DR: In this article, the existence of weak solutions for second-order boundary value problem of impulsive dynamic equations on time scales by employing critical point theory is studied. But weak solutions are not sufficient.
Abstract: We study the existence of weak solutions for second-order boundary value problem of impulsive dynamic equations on time scales by employing critical point theory.
3 citations