相关论文: A moving boundary problem motivated by electric br…
Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the…
We consider the hydrodynamics of an incompressible fluid on a 2D periodic domain. There exists a family of stationary solutions with vorticity given by $\Omega^*=\alpha\cos (\mathbf{p} \cdot \mathbf{x} )+\beta \sin (\mathbf{p} \cdot…
We are interested in evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a…
We consider Euler flows on two-dimensional (2D) periodic domain and are interested in the stability, both linear and nonlinear, of a simple equilibrium given by the 2D Taylor-Green vortex. As the first main result, numerical evidence is…
We show that a steady-state solution ${\bf U}$ to the system of equations of a Navier-Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator $\cal L$ has a part of the spectrum in the half-plane…
We investigate the linear stability of inviscid columnar vortices with respect to finite energy perturbations. For a large class of vortex profiles, we show that the linearized evolution group has a sub-exponential growth in time, which…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
Spectral properties of Toeplitz operators and their finite truncations have long been central in operator theory. In the finite dimensional, non-normal setting, the spectrum is notoriously unstable under perturbations. Random perturbations…
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…
We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method,…
In the present work we revisit the problem of the generalized Korteweg-de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergence of blow-up solutions, as traveling waveforms lose their…
In this paper we study the behaviour of the continuous spectrum of the Laplacian on a complete Riemannian manifold of bounded curvature under perturbations of the metric. The perturbations that we consider are such that its covariant…
The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a…
The Neumann problem in two-dimensional domain with a narrow slit is studied. The width of the slit is a small parameter. The complete asymptotic expansion for the eigenvalue of the perturbed problem converging to a simple eigenvalue of the…
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…
In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau…
We study the behaviour of eigenvalues, below the bottom of the essential spectrum, of the Laplacian under finite Riemannian coverings of complete and connected Riemannian manifolds. We define spectral stability and instability of such…
An initial-value problem for arbitrary small 3D vorticity perturbations imposed on a free shear flow is considered. The viscous perturbation equations are then combined in terms of the vorticity and velocity, and are solved by means of a…