Spectral Properties and Stability of Self-Similar Wave Maps
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The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite-dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose inverse is by defi ...
The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...
Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the pow ...
This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the kth (generalized) eigenvalue decays exponentially in root k, provided that the involved operator A gener ...
We study the Cauchy problem for the half Ginzburg- Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coecients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is ...
Two-dimensional (2D) flows can be controlled efficiently using spanwise "waviness," i.e., a control (e.g., wall blowing and suction or wall deformation) that is periodic in the spanwise direction. This study tackles the global linear stability of 2D flows ...
This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the ...
We review spectral methods for the solution of hyperbolic problems. To keep the discussion concise, we focus on Fourier spectral methods and address key issues of accuracy, stability, and convergence of the numerical approximations. Polynomial methods are ...
We show that concurrent atomistic/continuum displacement-coupling methods are inherently unstable in the context of fully dynamic problems at finite temperature. The fundamental origin of the instability is the displacement coupling of two material descrip ...
In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction, of strength beta, centred at 0 (the bottom of the confining parabolic potential), that was rigorou ...