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Unique localization of unknown boundaries in a conducting medium from boundary measurements

Bruno Canuto (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of localizing an inaccessible piece I of the boundary of a conducting medium Ω , and a cavity D contained in Ω , from boundary measurements on the accessible part A of ∂ Ω . Assuming that g ( t , σ ) is the given thermal flux for t , σ ∈ ( 0 , T ) × A , and that the corresponding output datum is the temperature u ( T 0 , σ ) measured at a given time T 0 for σ ∈ A out ⊂ A , we prove that I and D are uniquely localized from knowledge of all possible pairs of input-output data ( g , u ( T 0 ) ∣ A out ) . The same result holds when a mean value of the temperature...

Unique Localization of Unknown Boundaries in a Conducting Medium from Boundary Measurements

Bruno Canuto (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of localizing an inaccessible piece I of the boundary of a conducting medium Ω, and a cavity D contained in Ω, from boundary measurements on the accessible part A of ∂Ω. Assuming that g(t,σ) is the given thermal flux for (t,σ) ∈ (0,T) x A, and that the corresponding output datum is the temperature u(T0,σ) measured at a given time T0 for σ ∈ Aout ⊂ A, we prove that I and D are uniquely localized from knowledge of all possible pairs of input-output data ( g , u ( T 0 ) ∣ A out ) . The same result...

Variational convergence of nonlinear diffusion equations: applications to concentrated capacity problems with change of phase

Giuseppe Savaré, Augusto Visintin (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study a variational formulation for a Stefan problem in two adjoining bodies, when the heat conductivity of one of them becomes infinitely large. We study the «concentrated capacity» model arising in the limit, and we justify it by an asymptotic analysis, which is developed in the general framework of the abstract evolution equations of monotone type.

Variational problems with free boundaries for the fractional Laplacian

Luis Caffarelli, Jean-Michel Roquejoffre, Yannick Sire (2010)

Journal of the European Mathematical Society

We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.

Vectorial quasilinear diffusion equation with dynamic boundary condition

Nakayashiki, Ryota (2017)

Proceedings of Equadiff 14

In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S) ε with a nonnegative constant ε , and for any ε ≥ 0 , (S) ε can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain Ω , and the parabolic equation on the boundary Γ : = ∂ Ω , having a sufficient smoothness. The objective of this study is to establish a mathematical method, which can...

Weak uniqueness and partial regularity for the composite membrane problem

Sagun Chanillo, Carlos E. Kenig (2008)

Journal of the European Mathematical Society

We study the composite membrane problem in all dimensions. We prove that the minimizing solutions exhibit a weak uniqueness property which under certain conditions can be turned into a full uniqueness result. Next we study the partial regularity of the solutions to the Euler–Lagrange equation associated to the composite problem and also the regularity of the free boundary for solutions to the Euler–Lagrange equations.

Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

Patricio Cumsille, Takéo Takahashi (2008)

Czechoslovak Mathematical Journal

In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space ℝ d , d = 2 or 3 . The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary...

Currently displaying 381 – 400 of 419