Related papers: Evolutionary equations with state-dependent delay

In this paper, we consider energy decay estimates for the following nonlinear evolution problem $$\begin{split} [P(u_t(t))]_t + A u(t) + B(t , x , u_t(t)) =0,\quad t\in J=(0,\infty), \end{split}$$ under suitable assumptions on the…

The "separant" of the evolution equation u_t=F, where F is some differentiable function of the derivatives of u up to order m is the partial derivative \partial F}/{\partial u_m} where u_m={\partial^m u}/{\partial x}^m. We apply the formal…

This paper is a continuation of [13], where new variational principles were introduced based on the concept of anti-selfdual (ASD) Lagrangians. We continue here the program of using these Lagrangians to provide variational formulations and…

We consider the following evolutionary Hamilton-Jacobi equation with initial condition: \begin{equation*} \begin{cases} \partial_tu(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\\ u(x,0)=\phi(x). \end{cases} \end{equation*} Under some assumptions on…

In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are…

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…

Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…

In this paper, we establish a Liouville type theorem for the homogeneous dual fractional parabolic equation \begin{equation} \partial^\alpha_t u(x,t)+(-\Delta)^s u(x,t) = 0\ \ \mbox{in}\ \ \mathbb{R}^n\times\mathbb{R} . \end{equation} where…

We investigate state dependent delay differential equations with distributed memory, combining discrete state dependent delays and a convolution type memory operator. Under Lipschitz type assumptions on the delay, kernel, and nonlinear…

We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…

We investigate the regularity of local weak solutions to evolution equations of the form \[…

We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…

We consider an initial value problem for time-fractional evolution equation in Banach space $X$: $$ \pppa (u(t)-a) = Au(t) + F(t), \quad 0<t<T. \eqno{(*)} $$ Here $u: (0,T) \rrrr X$ is an $X$-valued function defined in $(0,T)$, and $a \in…

We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the…

We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…

A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state-dependent delay and discuss…

We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of…

Real-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems…

We study the regularity of weak solutions to evolution equations with distributed order fractional time derivative. We prove a weak Harnack inequality for nonnegative weak supersolutions and H\"older continuity of weak solutions to this…

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…