We study the Cauchy problem for the equation of the form (*) ü(t) + (αA+ B)u̇(t) + (A+G)u(t) = 0 where A, B, and G are operators in a Hilbert space H with A selfadjoint, σ(A) = [0,∞), B > 0 bounded, and G symmetric and Asubordinate in a certain sense. Spectral properties of the corresponding operator pencil L(λ) := λI +λ(αA+B) + A+G are studied, and existence and uniqueness of generalized and cl...

in this paper, the detector of moving target in mimo radar with widely separated antenna in the presence of α-stable clutter is proposed. due to the complexity of unknown parameter estimation in the presence of target, the rao test is applied. the α-stable model is a general model that can applied to different environments with appropriate selection of parameters. the problem with this model is...

We consider the mass-subcritical Hartree equation with a homogeneous kernel, in the space of square integrable functions whose Fourier transform is integrable. We prove a global well-posedness result in this space. On the other hand, we show that the Cauchy problem is not even locally wellposed if we simply work in the space of functions whose Fourier transform is integrable. Similar results ar...

Abstract. We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n suf...

Abstract In this paper, we study the Cauchy problems for quasilinear hyperbolic inequalities with nonlocal singular source term and prove nonexistence of global weak solutions in homogeneous nonhomogeneous cases by test function method.

The stability is one of the most basic requirement for the numerical model, which is mostly elaborated for the linear problems. In this paper we analyze the stability notions for the nonlinear problems. We show that, in case of consistency, both the N-stability and Kstability notions guarantee the convergence. Moreover, by using the Nstability we prove the convergence of the centralized Crank--...

s of MMA2013 & AMOE2013, May 27–30, 2013, Tartu, Estonia c © 2013 University of Tartu A CONFORMAL MAPPING METHOD IN INVERSE OBSTACLE SCATTERING RAINER KRESS Institut für Numerische und Angewandte Mathematik, Universität Göttingen Lotzestraße 16–18, 37083 Göttingen, Germany E-mail: [email protected] In a series of papers Akduman [1], Haddar [2] and Kress [5] have employed a conformal ...

Abstract: The paper concerns the existence of weak solutions to the Cahn-Hilliard-Gurtin system coupled with nonstationary elasticity. The system describes phase separation process in elastically stressed material. It generalizes the Cahn-Hilliard equation by admitting a more general structure and by coupling diffusive and elastic effects. The system is studied with the help of a singularly per...