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We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.

A two-species cooperative Lotka-Volterra system of degenerate parabolic equations.

Sun, Jiebao, Zhang, Dazhi, Wu, Boying (2011)

Abstract and Applied Analysis

A two-step Monge-Ampère procedure for solving a fourth order PDE for affine hypersurfaces with constant curvature.

Udo Simon, An-Min Li, Bohui Chen (1997)

Journal für die reine und angewandte Mathematik

A unified approach to a posteriori error estimation using element residual methods.

Mark Ainsworth, J. Tinsley Oden (1993)

Numerische Mathematik

A unified optimality condition for eigenvalue problems

Wen Bin Liu, Julio E. Rubio (1993)

Kybernetika

A uniform boundary Harnack inequality on non-tangentially accessible domains.

Rainer Wittmann (1988)

Journal für die reine und angewandte Mathematik

A uniformly accurate finite volume discretization for a convection-diffusion problem.

Wollstein, Dirk, Linß, Torsten, Roos, Hans-Görg (2002)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

A uniformly controllable and implicit scheme for the 1-D wave equation

Arnaud Münch (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters $h$ and $Δ t$ . We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order $h^{2}$ and $Δ t^{2}$ . Using a discrete...

A uniformly controllable and implicit scheme for the 1-D wave equation

Arnaud Münch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters h and Δt. We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order h2 and Δt2. Using...

A unilateral thermoelastic Stefan-type problem

Rodrigues, José Francisco (1988)

Portugaliae mathematica

A unique continuation property for linear elliptic systems and nonresonance problems.

Anane, A., Chakrone, O., El Allali, Z., Hadi, I. (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A unique continuation theorem for the wave equation in the exterior of a characteristic cone

F. G. Friedlander (1982/1983)

Séminaire Équations aux dérivées partielles (Polytechnique)

A uniqueness criterion for the solution of the stationary Navier-Stokes equations

Giovanni Prouse (1989)

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

A uniqueness criterion is given for the weak solution of the Navier-Stokes equations in the stationary case. Precisely, it is proved that, for a generic known term, there exists one and only one solution such that the mechanical power of the corresponding flow is maximum and that this maximum is "stable" in an appropriate sense.

A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum

Jens Frehse, Sonja Goj, Josef Málek (2005)

Applications of Mathematics

We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities $ρ_{i}$ of the fluids and their velocity fields $u^{(i)}$ are prescribed at infinity: $ρ_{i} |_{\infty} = ρ_{i \infty} > 0$ , $u^{(i)} |_{\infty} = 0$ . Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution, namely $ρ_{i} \equiv ρ_{i \infty}$ , $u^{(i)} \equiv 0$ , $i = 1, 2$ .

A uniqueness result for an inverse problem

Robert Dalmasso (2004)

Annales Polonici Mathematici

We establish a uniqueness result for an overdetermined boundary value problem. We also raise a new question.

A uniqueness result for the continuity equation in two dimensions

Giovanni Alberti, Stefano Bianchini, Gianluca Crippa (2014)

Journal of the European Mathematical Society

We characterize the autonomous, divergence-free vector fields $b$ on the plane such that the Cauchy problem for the continuity equation $\partial_{t} u + \frac{.}{\dot{}} (b u) = 0$ admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential $f$ associated to $b$ . As a corollary we obtain uniqueness under the assumption that the curl of $b$ is a measure. This result can be extended to certain non-autonomous vector fields $b$ with bounded divergence....

A uniqueness result in the theory of stereo vision : coupling shape from shading and binocular information allows unambiguous depth reconstruction

Antonin Chambolle (1994)

Annales de l'I.H.P. Analyse non linéaire

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