Related papers: Semi-uniform stability of operator semigroups and …
We consider the semilinear damped wave equation $\partial_{tt}^2 u(x,t)+\gamma(x)\partial_t u(x,t)=\Delta u(x,t)-\alpha u(x,t)-f(x,u(x,t))$. In this article, we obtain the first results concerning the stabilization of this semilinear…
In this paper we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to the linear problem with decay rate depending on…
We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…
We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…
Relatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandi\'c, Kramar-Fijav\v{z}, and the second-named author, in order to make the theory of one-parameter operator semigroups available in the setting of…
We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of…
Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution operators of singular integral equations. Such equations…
We consider the wave equation with a boundary condition of memory type. Under natural conditions on the acoustic impedance $\hat{k}$ of the boundary one can define a corresponding semigroup of contractions (Desch, Fasangova, Milota, Probst…
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…
An asymptotic preserving and energy stable scheme for the Euler-Poisson system under the quasineutral scaling is designed and analysed. Correction terms are introduced in the convective fluxes and the electrostatic potential, which lead to…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
We use the uniform semiclassical approximation in order to derive the fidelity decay in the regime of large perturbations. Numerical computations are presented which agree with our theoretical predictions. Moreover, our theory allows to…
This work presents a comprehensive study of the microlocal energy decomposition and propagation of singularities for semiclassically adjusted dissipative pseudodifferential operators. The analysis focuses on the behavior of energy…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
We present the new results on stability and semi-classical limit in a semiconductor full quantum hydrodynamic (FQHD) model with non-flat doping profile. The FQHD model can be used to analyze the thermal and quantum influences on the…
We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…
An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence of time damped perturbations with power-law asymptotics is investigated. The particular solutions tending at…