It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing linearized system. However, this classical result does not generalize to infinite-dimensional systems. In paper, we restrict ourselves semilinear systems, and show exact system implies The restrictions concerning operator are similar those found in literature about stability analysis

We investigate the features arising from hydrodynamic effects in graphene and phosphorene devices with finite heat sources, using ab initio calculations to go beyond Callaway's model inform a full linearized scattering operator, solving phonon Boltzmann transport equation through energy-based deviational Monte Carlo methods. explain mechanisms that create those features, showing boundary relati...

In this work, we are interested in the spectrum of the diffusively excited granular gases equation, in a space inhomogeneous setting, linearized around an homogeneous equilibrium. We perform a study which generalizes to a non-hilbertian setting and to the inelastic case the seminal work of Ellis and Pinsky [8] about the spectrum of the linearized Boltzmann operator. We first give a precise loca...

A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for stable recovery of the migration amplitude...

Seismic data are commonly modeled by a linearization around a smooth background medium in combination with a high frequency approximation. The perturbation of the medium coefficient is assumed to contain the discontinuities. This leads to two inverse problems, first the linearized inverse problem for the perturbation, and second the estimation of the background, which is a priori unknown (veloc...

In a recent interesting paper, GIDAS, NI, and NIRENBERG [2] proved that positive solutions of the Dirichlet problem for second-order semi-linear elliptic equations on balls must themselves be spherically symmetric functions. Here we consider the bifurcation problem for such solutions. Specifically, we investigate the ways in which the symmetric solution can bifurcate into a nonsymmetric solutio...

In this paper, we study the existence and uniqueness of a degenerate parabolic equation, with nonhomogeneous boundary conditions, coming from the linearization of the Crocco equation [12]. The Crocco equation is a nonlinear degenerate parabolic equation obtained from the Prandtl equations with the so-called Crocco transformation. The linearized Crocco equation plays a major role in stabilizatio...

We provide a linear analysis on normal modes of the spin Boltzmann equation proposed by Weickgenannt et al. [Phys. Rev. D 104, 016022 (2021)], where nondiagonal or polarized part transition rate is neglected to ensure Hermitian property linearized collision operator. As an instrumental element kinetic theory, conservation total angular momentum explicitly considered; thus, our relevant recent i...

In this paper, we deal with the inverse problem of shape reconstruction inclusions in elastic bodies. The main idea is based on monotonicity property Neumann-to-Dirichlet operator presented a former article authors. Thus, introduce so-called standard as well linearized tests order to detect and reconstruct inclusions. addition, compare these methods each other present several numerical test exa...