Related papers: Systems of parabolic equations with delays: Contin…
Optimal second-order regularity in the space variables is established for solutions to Cauchy-Dirichlet problems for nonlinear parabolic equations and systems of $p$-Laplacian type, with square-integrable right-hand sides and initial data…
We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…
Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…
Aim of this paper is to extend the continuous dependence estimates proved in \cite{JK1} to quasi-monotone systems of fully nonlinear second-order parabolic equations. As by-product of these estimates, we get an H\"older estimate for bounded…
The autor considers an initial-boundary value problem for the nonstationary Stokes system in an angle, where Dirichlet and Neumann conditions are prescribed on the diferent sides of the angle. The major part of the paper deals with the…
Synchronization in an array of mutually coupled systems with a finite time-delay in coupling is studied using Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by…
We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent…
Stability analysis is performed for a linear differential equation with two delays. Geometric arguments show that when the two delays are rationally dependent, then the region of stability increases. When the ratio has the form 1/n, this…
This paper deals with a unifying approach to the problems of computing the admissible sets of parametrical multi perturbations in appropriate bounded sets such that some fundamental properties of parameter-varying linear dynamic systems are…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
Regimes with a singular peaking for a wide class of quasilinear second order parabolic equations are studied. On the basis of energy methods, precise estimates of a final profile of a weak solution in a neighborhood of the peaking time are…
In this paper second-order elliptic and parabolic partial differential systems are considered on $C^1$ domains. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
We provide a class of methods for the identification of a linear system with delay of the shape $x^{(n)}(t) = \sum_{i=0}^{n-1}a_{i}x^{(i)}(t) + bu(t-h)$. They allow the simultaneous identification of the parameters and delay, the…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the ``Leitmotiv'' for the following. A reduced order model is…
Averaging principle for abstract non-autonomous parabolic evolution equations governed by time-dependent family of positive sectorial operators is proved. Apart from linear case also a nonlinear version for continuous perturbations is…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…