Results 1 - 10 of 1718
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[en] For a scalar field the Casimir forces, acting on parallel plates in models with a compact subspace, are investigated. On the plates the field obeys the Robin boundary conditions. Depending on the values of the coefficients in the boundary conditions, the forces can be either attractive or repulsive. In models with a homogeneous compact subspace they are the same for both the plates. In special cases of Dirichlet and Neumann boundary conditions the Casimir forces are attractive. As applications of general results, we consider special cases with the subspaces S1 and S2
[en] Scattering through a straight two-dimensional quantum waveguide R×(0,d) with Dirichlet boundary conditions on (R−*×(y=0))∪(R+*×(y=d)) and Neumann boundary condition on (R−*×(y=d))∪(R+*×(y=0)) is considered using stationary scattering theory. The existence of a matching conditions solution at x = 0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown
[en] We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet–Neumann map. We extend here the stability result obtained by Alessandrini and Vessella (Alessandrini G and Vessella S 2005 Lipschitz stability for the inverse conductivity problem Adv. Appl. Math. 35 207–241), where the authors considered the piecewise constant isotropic case. (paper)
[en] Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that this problem is well-posed in L2-setting. Existence and regularity results are established, as well as an analog of the maximum principle.
[en] Entire Dirichlet series with real coefficients are studied in the case when the sequence of sign changes of the coefficients satisfies the Levinson condition. The best possible lower estimate for the growth rate of a Dirichlet series on the positive half-axis is obtained. Bibliography: 25 titles.
[en] Here we consider the problem of the asymptotic expansion of the Laplace-Dirichlet integral. In homogenization theory such an integral represents the energy, and in general depends on the cohomology class. Here the asymptotic behaviour of this integral is found. The full text will appear in Functional Analysis and Applications, 1990, No.2. (author). 3 refs
[en] Highlights: • Kleinian ultra-elliptic function formulas for two-phase solutions of the focusing NLSE. • Theta function formulas for two-phase solutions with explicit construction of parameters. • Real loci of the Dirichlet eigenvalues parametrized by wave amplitude and wavenumber. • Simple formulas for the extrema of the modulus of the two-phase solution. An effective integration method based on the classical solution of the Jacobi inversion problem, using Kleinian ultra-elliptic functions and Riemann theta functions, is presented for the quasi-periodic two-phase solutions of the focusing cubic nonlinear Schrödinger equation. Each two-phase solution with real quasi-periods forms a two-real-dimensional torus, modulo a circle of complex-phase factors, expressed as a ratio of theta functions associated with the Riemann surface of the invariant spectral curve. The initial conditions of the Dirichlet eigenvalues satisfy reality conditions which are explicitly parametrized by two physically-meaningful real variables: the squared modulus and a scalar multiple of the wavenumber. Simple new formulas for the maximum modulus and the minimum modulus are obtained in terms of the imaginary parts of the branch points of the Riemann surface.
[en] In the present paper, with the aid of the techniques of micro-local analysis, a regularity theorem of the solutions to Dirichlet problem for a class of nonlinear degenerate elliptic equations is given. (author). 8 refs
[en] This paper is concerned with distributed and Dirichlet boundary controls of semilinear parabolic equations, in the presence of pointwise state constraints. The paper is divided into two parts. In the first part we define solutions of the state equation as the limit of a sequence of solutions for equations with Robin boundary conditions. We establish Taylor expansions for solutions of the state equation with respect to perturbations of boundary control (Theorem 5.2). For problems with no state constraints, we prove three decoupled Pontryagin's principles, one for the distributed control, one for the boundary control, and the last one for the control in the initial condition (Theorem 2.1). Tools and results of Part 1 are used in the second part to derive Pontryagin's principles for problems with pointwise state constraints