Related papers: Spectral stability of the Steklov problem
We explore stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign.…
We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schr\"odinger operators on compact Riemannian surfaces with boundary. For the zero potential, we recover the well-known spectral…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
We deal with the as yet unresolved exponential stability problem for Beck's Problem on a metric star graph with three identical edges. The edges are stretched Euler--Bernoulli beams which are simply supported with respect to the outer…
We study the counting function of Steklov eigenvalues on compact manifolds with boundary and obtain its upper bound involving the leading term of Weyl's law. Our estimate can be viewed as a weakened version of P\'{o}lya's Conjecture in the…
We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we…
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
Given a conformal action of a discrete group on a Riemann surface, we study the maximization of Laplace and Steklov eigenvalues within a conformal class, considering metrics invariant under the group action. We establish natural conditions…
We study boundary value problems for bounded uniform domains in $\mathbb{R}^n$, $n\geq 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincar\'e inequalities with trace terms and uniform constants for uniform…
We consider the sum of two large Hermitian matrices $A$ and $B$ with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is…
In this thesis the Cauchy problem and in particular the question of singularity formation for co--rotational wave maps from 3+1 Minkowski space to the three--sphere $S^3$ is studied. Numerics indicate that self--similar solutions of this…
We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral…
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we…
In this article, we investigate the weighted Steklov eigenvalue problem and the weighted Schr\"odinger--Steklov eigenvalue problem in outward cuspidal domains. We prove the solvability of these spectral problems in both linear and…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
?In this work, we study the orbital stability of stationary solutions to the relativistic Vlasov-Manev system. This system is a kinetic model describing the evolution of a stellar system subject to its own gravity with some relativistic…
In the scalar Swift-Hohenberg equation with quadratic-cubic nonlinearity, it is known that symmetric pulse solutions exist for certain parameter regions. In this paper we develop a method to determine the spectral stability of these…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for…
Rozowsky, Volkas and Wali recently found interesting numerical solutions to the field equations for a gauged U1xU1 scalar field model. Their solutions describe a reflection-symmetric domain wall with scalar fields and coupled gauge…