نتایج جستجو برای: ‎U‎nkown boundary ‎condition

تعداد نتایج: 458496  

2005
N. S. MERA L. ELLIOTT D. B. INGHAM D. LESNIC

In this paper we consider the determination of the shape of an unkown portion of the boundary of a three-dimensional solution domain from Cauchy data on the remaining portion of the boundary. This problem arises in the study of quantitative non-destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused ...

Journal: :Japanese Journal of Radiological Technology 1982

2006
Henrik Shahgholian HAYK MIKAYELYAN HENRIK SHAHGHOLIAN

We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫ BR |∇v|dx + Per({v > 0}), 1 < p < ∞, over the set {v ∈ H 0 (BR)| v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.

2014

We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...

Journal: :I. J. Bifurcation and Chaos 2005
Neus Cónsul Angel Jorba

We consider a diffusion equation on a domain Ω with a cubic reaction at the boundary. It is known that there are no patterns when the domain Ω is a ball, but the existence of such patterns is still unkown in the more general case in which Ω is convex. The goal of this paper is to present numerical evidence of the existence of nonconstant stable equilibria when Ω is the unit square. These patter...

Journal: :SIAM Journal of Applied Mathematics 2001
Isom H. Herron

Abstract. The problem of Rayleigh–Bénard convection with internal heat sources and a variable gravity field is treated. For the case of stress-free boundary conditions, it is proved that the principle of exchange of stabilities holds as long as the product of gravity field and the integral of the heat sources is nonnegative throughout the layer. The proof is based on the idea of a positive oper...

2008
Robert Denk Reinhard Racke Yoshihiro Shibata

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by ...

2013
George Avalos Irena Lasiecka GEORGE AVALOS

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. LAGNESE, Boundary Stabilization of Twin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case—where rotational forces are neglected—in [Z. ...

2015
MAX ENGELSTEIN

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro [KT06] and prove a sharp Hölder regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must establish non-degeneracy by means of monotonicity formulae.

Journal: :Progress of Theoretical Physics 2011

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