Related papers: Optimal time delays in a class of reaction-diffusi…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated…
We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…
We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear…
The equivalence of time-optimal and distance-optimal control problems is shown for a class of parabolic control systems. Based on this equivalence, an approach for the efficient algorithmic solution of time-optimal control problems is…
We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…
We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…
We prove sharp estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations on a bounded domain subject to a homogeneous Dirichlet boundary condition. Important special cases are the…
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition…
This article deals with variational optimal-control problems on time scales in the presence of delay in the state variables. The problem is considered on a time scale unifying the discrete, the continuous and the quantum cases. Two examples…
The aim of this work is to make a survey on recent sufficient optimality conditions for optimal control problems with time delays in both state and control variables. The results are obtained by transforming delayed optimal control problems…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…