Related papers: Liouville equation under perturbation
This article is devoted to the regular fractional Sturm--Liouville eigenvalue problem. Applying methods of fractional variational analysis we prove existence of countable set of orthogonal solutions and corresponding eigenvalues. Moreover,…
This paper is concerned with the large time behavior of the solution to the Cauchy problem for the elastic wave equations. In particular, optimal $L^{2}$ estimates of the elastic waves are obtained in the sense that the upper and lower…
Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
We establish Liouville type theorems for degenerate conformally invariant equations.
We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
Using Mourre theory, we obtain low frequency resolvent estimates with sharp weights for long range metric perturbations of the flat Laplacian.
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…
Solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent Riemannian metric.
We consider the stability of the two branches of non-extremal enhancon solutions. We argue that one would expect a transition between the two branches at some value of the non-extremality, which should manifest itself in some instability.…
We discuss two approaches to study the long-time behaviour and infinite-time behaviour of solutions for integrable hamiltonian systems under small stochastic perturbations. Then we compare these results with those for deterministic…
We use the integral by parts to get a Liouville type theorem for a class quasilinear $p$-Laplace type equation on the sphere, this $p$-Laplace type equation arises from the study of asymptotic behavior near the origin for the semi-linear…
We construct solutions of Schr\"odinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solutions are global, with non-zero $L^2$ norms, and are…
In this paper, we combine the method of multiple scales and the method of matched asymptotic expansions to construct uniformly-valid asymptotic solutions to autonomous and non-autonomous difference equations in the neighbourhood of a…
We develop a self-consistent version of perturbation theory in Liouville space which seeks to combine the advantages of master equation approaches in quantum transport with the nonperturbative features that a self-consistent treatment…
We study finite total curvature solutions of the Liouville equation $\Delta u+e^{2u}=0$ on a complete surface $(M,g)$ with nonnegative Gauss curvature. It turns out that the asymptotic behavior of the solution separates two extremal cases:…
In a recent paper, we established optimal Liouville-type theorems for conformally invariant second-order elliptic equations in the Euclidean space. In this work, we prove an optimal Liouville-type theorem for these equations in the…
In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum…
The Cauchy problem for a quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For some simplified formulation of the problem, a criterion for the…
In this paper the small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem. The analysis results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that…