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The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…

We establish linearized well-posedness of the Triple-Deck system in Gevrey-$\frac32$ regularity in the tangential variable, under concavity assumptions on the background flow. Due to the recent result \cite{DietertGV}, one cannot expect a…

We consider the problem of spectral stability of traveling wave solutions $u=\gamma(x-Wt)$ for a system of viscous conservation laws $\partial_t u + \partial_x F(u) = \partial^2_x u$. Such solutions correspond to heteroclinic trajectories…

This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…

Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedekind domain that encodes the following invariants: (i) the…

Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…

Let $R$ be a 3-dimensional complete local Gorenstein isolated singularity. For a basic maximal modifying $R$-module $M$, we construct a wall-and-chamber structure, denoted by ${\sf Cone}(M)$ and called the mutation cone of $M$, in the real…

We consider de Finetti's problem for spectrally one-sided L\'evy risk models with control strategies that are absolutely continuous with respect to the Lebesgue measure. Furthermore, we consider the version with a constraint on the time of…

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…

We study (generalized) cones over metric spaces, both in Riemannian and Lorentzian signature. In particular, we establish synthetic lower Ricci curvature bounds \`a la Lott-Villani-Sturm and Ohta in the metric measure case, and \`a la…

In this paper we consider well-posedness properties of vector optimization problems with objective function $f: X \to Y$ where $X$ and $Y$ are Banach spaces and $Y$ is partially ordered by a closed convex pointed cone with nonempty…

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…

We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special…

This paper formalises the concepts of weakly and weakly regularly persistent input trajectory as well as their link to the Observability Grammian and the existence and uniqueness of solutions of Moving Horizon Estimation (MHE) problems.…

Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form…

Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…

Krein condition have been used as a qualitative result to show the M-indeterminacy of some kind of densities. In this work we use results from the theory of the Hilbert transform to construct families of densities having all the same finite…

We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…