摘要 :
We prove existence and uniqueness of solutions for a class of infinitely delayed stochastic evolution equations with multiplicative noise term where A is the generator of an analytic semigroup on a UMD Banach space E and F and G a...
展开
We prove existence and uniqueness of solutions for a class of infinitely delayed stochastic evolution equations with multiplicative noise term where A is the generator of an analytic semigroup on a UMD Banach space E and F and G are functions from the history of the system satisfying Lipschitz conditions. This paper is based on recent work of van Neerven et al., developing the theory of abstract stochastic evolution equations in UMD Banach spaces.
收起
摘要 :
In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form...
展开
In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research.
收起
摘要 :
The main target of this paper is to present criteria (adapted from the point delay systems) for the different kinds of stability, boundedness and existence of a stochastic attractor for a class of distributed delay differential st...
展开
The main target of this paper is to present criteria (adapted from the point delay systems) for the different kinds of stability, boundedness and existence of a stochastic attractor for a class of distributed delay differential stochastic equations. The new results are based on a technique of reduction of distributed delay to a lumped delay and Mao criteria for point delay equations. (c) 2006 Elsevier B.V. All rights reserved.
收起
摘要 :
Some results are given concerning the behavior of the solutions for scalar first order linear autonomous delay as well as neutral delay differential equations. These results are obtained by the use of two distinct real roots of th...
展开
Some results are given concerning the behavior of the solutions for scalar first order linear autonomous delay as well as neutral delay differential equations. These results are obtained by the use of two distinct real roots of the corresponding characteristic equation.
收起
摘要 :
? 2023 Elsevier Inc.In this paper, we give a brief summary of fractal calculus. Fractal functional differential equations are formulated as a framework that provides a mathematical model for the phenomena with fractal time and fra...
展开
? 2023 Elsevier Inc.In this paper, we give a brief summary of fractal calculus. Fractal functional differential equations are formulated as a framework that provides a mathematical model for the phenomena with fractal time and fractal structure. Fractal retarded, neutral, and renewal delay differential equations with constant coefficients are solved by the method of steps and using Laplace transform. The graphs of solutions are given to show the details.
收起
摘要 :
We study a second order state-dependent delay equation with an in general unbounded delay that describes an idealized one-dimensional motion. Although governed by a negative feedback mechanism, the set of equilibria, formed by the...
展开
We study a second order state-dependent delay equation with an in general unbounded delay that describes an idealized one-dimensional motion. Although governed by a negative feedback mechanism, the set of equilibria, formed by the so called constant velocity solutions, is unstable and a new kind of instability, called the escaping instability, evolves.
收起
摘要 :
A one dimensional heat equation in a semi-infinite medium controlled through a heat source depending on the delayed heat flux at the extremum is studied. By reducing the problem to a delayed Volterra integral equation with a weakl...
展开
A one dimensional heat equation in a semi-infinite medium controlled through a heat source depending on the delayed heat flux at the extremum is studied. By reducing the problem to a delayed Volterra integral equation with a weakly singular kernel, we find conditions on the initial datum and on the source term of the equation to control the asymptotic behaviour of the mean temperatures.
收起
摘要 :
In this paper we present a new method for deriving Ito stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same...
展开
In this paper we present a new method for deriving Ito stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME, we prove that they are equivalent both in distribution, and in sample paths they produce. This allows us to formulate an algorithmic approach to deriving equivalent Ito SDDEs with a smaller number of noise variables, which increases the computational speed of simulating stochastic delayed systems. The new method is illustrated on a simple model of two interacting species and a model with bistability, and in both cases it shows excellent agreement with the results of direct stochastic simulations, while also demonstrating a much superior speed of performance.
收起
摘要 :
We show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The ...
展开
We show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The other part, called the pseudocontinuous spectrum, accumulates near criticality and converges after rescaling to a set of spectral curves, called the asymptotic continuous spectrum. We show that the spectral curves and str ong spectral points provide a complete description of the spectrum for sufficiently large delay and can be comparatively easily calculated by approximating expressions.
收起
摘要 :
In this paper we investigate local and global existence as well as asymptotic behavior of the solution for a class of abstract; (hyperbolic) quasilinear equations perturbed by bounded delay operators. We assume that the leading op...
展开
In this paper we investigate local and global existence as well as asymptotic behavior of the solution for a class of abstract; (hyperbolic) quasilinear equations perturbed by bounded delay operators. We assume that the leading operator is of bounded variation in time. In the last section, the abstract results are applied on a heat conduction model.
收起
原文获取