相关论文: Stability of the essential spectrum for 2D--transp…
We investigate the spectral properties of the time-dependent linear transport equation with bounce-back boundary conditions. A fine analysis of the spectrum of the streaming operator is given and the explicit expression of the strongly…
We investigate the spectral properties of a class of weighted shift semigroups associated to abstract transport equations with a Lipschitz--continuous vector field with no--reentry boundary conditions. We illustrate our results with various…
This paper provides a new tauberian approach to the study of quantitative time asymptotics of collisionless transport semigroups with general diffuse boundary operators. We obtain an (almost) optimal algebraic rate of convergence to…
This paper considers and extends spectral and scattering theory to dissipative symmetric systems that may have zero speeds and in particular to strictly dissipative boundary conditions for Maxwell's equations. Consider symmetric systems…
This paper gives a spectral approach to time asymptotics of collisionless transport semi-groups with general diffuse boundary operators. The strong stability of the invariant density is derived from the classical Ingham theorem. A recent…
Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend…
For Schr\"odinger operator $H=-\Delta+ V({\mathbf x})\cdot$, acting in the space $L_2(\mathbb R^d)\,(d\ge 3)$, necessary and sufficient conditions for semi-boundedness and discreteness of its spectrum.are obtained without assumption that…
We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity $\varepsilon$, permeability $\mu$ and conductivity $\sigma$, on finitely connected unbounded domains. The main result is…
We present $c_0$--semigroup generation results for the free streaming operator with abstract boundary conditions. We recall some known results on the matter and establish a general theorem. We motivate our study with a lot of examples and…
Models describing transport and diffusion processes occurring along the edges of a graph and interlinked by its vertices have been recently receiving a considerable attention. In this paper we generalize such models and consider a network…
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity…
We consider general linear kinetic equations combining transport and a linear collision on the kinetic variable with a spatial weight that can vanish on part of the domain. The considered transport operators include external potential…
We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…
We studied the edge states and transverse electron focusing in the presence of spin-orbit interaction in a two dimensional electron gas. Assuming strong spin-orbit coupling we derived semiclassical quantization conditions to describe the…
We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to…
This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coefficient and for the full range of interaction potentials,…
The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar…
We study the issues of scaling and universality in spectral and transport properties of the infinite dimensional particle--hole symmetric (half-filled) Hubbard model within dynamical mean field theory. One of the simplest and extensively…