Related papers: Nonlinear evolution equations with exponentially d…
In this paper, we are devoted to consider the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroups theory and fixed point theorem, we establish some new existence theorems of…
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefore suitable in the sense of Scheffer and…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for $H^s$ initial data, $s>-1/2$, and for any $s_1<\min(3s+1,s+1)$, the difference of the nonlinear and linear evolutions is in $H^{s_1}$…
The main objective of this manuscript is to investigate the global behavior of the solutions to the viscoelastic wave equation with a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as a…
We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the…
Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…
Higher-order nonlinear time-evolution equations have widespread applications in science and engineering, such as in solid mechanics, materials science, and fluid mechanics. This paper mainly studies a direct time-parallel algorithm for…
This article investigates the existence and uniqueness of solutions to the second order Volterra integrodifferential equations with nonlocal and boundary conditions through its integral equivalent equations and fixed point of Banach.…
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…
We present implicit and explicit versions of a numerical algorithm for solving a Volterra integro-differential equation. These algorithms are an extension of our previous work, and cater for a kernel of general form. We use an appropriate…
The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric…
We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval,…
This paper is concerned with an integral equation that models discrete time dynamics of a population in a patchy landscape. The patches in the domain are reflected through the discontinuity of the kernel of the integral operator at a finite…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
This paper concerns the finite-time blow-up and asymptotic behaviour of solutions to nonlinear Volterra integrodifferential equations. Our main contribution is to determine sharp estimates on the growth rates of both explosive and…
A general formlulation for discrete-time quantum mechanics, based on Feynman's method in ordinary quantum mechanics, is presented. It is shown that the ambiguities present in ordinary quantum mechanics (due to noncommutativity of the…
We study the generalized fractional linear problem $D^{\nu}_{a+*} f(x) =A(x)f(x)+g(x)$, where $D^{\nu}$ is an arbitrary mixture of Caputo derivatives of order at most one and $A(x)$ a family of operators in a Banach space generating…
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines…