Related papers: Transverse instability of high frequency weakly st…
In this paper, we study the structurally nonlinear stability of supersonic contact discontinuities in three-dimensional compressible isentropic steady flows. Based on the weakly linear stability result and the $L^2$-estimates obtained by…
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…
As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further…
This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…
We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…
A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the…
We prove boundary higher integrability for the (spatial) gradient of \emph{very weak} solutions of quasilinear parabolic equations of the form $$ \left\{ \begin{array}{ll} u_t - div \mathcal{A}(x,t,\nabla u) = 0 &\quad \text{on} \ \Omega…
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a…
Answering a question left open in \cite{MZ2}, we show for general symmetric hyperbolic boundary problems with constant coefficients, including in particular systems with characteristics of variable multiplicity, that the uniform Lopatinski…
A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…
In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…
In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for Schr\"{o}dinger equation. The rigorous justification of increasing stability for the IBVP for Schr\"{o}dinger equation were…
In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Zakharov-Kuznetsov…
The rotation modified Kadomtsev Petviashvili equation which is also known as the Kadomtsev Petviashvili Ostrovsky equation, describes the gradual wave field diffusion in the transverse direction to the direction of the propagation of the…
We present a new form of intermittency, L\'evy on-off intermittency, which arises from multiplicative $\alpha$-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
The study of wave propagation outside bounded obstacles uncovers the existence of resonances for the Laplace operator, which are complex-valued generalized eigenvalues, relevant to estimate the long time asymptotics of the wave. In order to…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
In this work, we investigate the relation between bound states and quasinormal modes within black hole perturbation theory in the context of spectral instability. Our analysis indicates that the reliability of such spectral mapping…
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…