In this article the problem of an interface fracture between two isotropic linear elastic materials is studied within a continuum modeling framework, which incorporates important nanoscale effects. The proposed model of bi-material crack ascribes curvature-dependent surface tension to both the fracture surfaces and the solid-solid interface. Further, it uses as boundary conditions the jump mome...

We examine the existence of traveling wave solutions for a continuum neuronal network modeled by integro-differential equations. First, we consider a scalar field model with a general smooth firing rate function and a spatiotemporally varying stimulus. We prove that a traveling front solution that is locked to the stimulus exists for a certain interval of stimulus speeds. Next, we include a slo...

Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the br...

This work focuses on numerical methods for finding optimal investment, dividend payment, and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. The surplus is modeled by a regime-switching jump diffusion process subject to both regular and singular controls. Using dynamic programming principle, ...

We examine the existence of traveling wave solutions for a continuum neuronal network modeled by integro-differential equations. First, we consider a scalar field model with a general smooth firing rate function and a spatiotemporally varying stimulus. We prove that a traveling front solution that is locked to the stimulus exists for a certain interval of stimulus speeds. Next, we include a slo...

In this paper we consider the problem of constructing a well-posed state space model for a class of singular integro-diierential equations of neutral type. The work is motivated by the need to develop a framework for the analysis of numerical methods for designing control laws for aeroelastic and other uid/structure systems. Semigroup theory is used to establish existence and well-posedness res...

<p style='text-indent:20px;'>This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates include all cases Abel-type Firstly, existence, uniqueness and continuous dependence on true solution under local Lipschitz condition linear growth are d...

Keywords: Impulsive stochastic systems Integro-differential systems Schaefer's fixed point theorem Complete controllability a b s t r a c t This paper is concerned with the controllability of impulsive stochastic integro-differential systems. Sufficient conditions of complete controllability for impulsive stochastic integro-differential systems are obtained by using Schaefer's fixed point theor...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

A boundary value problem for fractional integro-differential equations with weakly singular kernels is considered. The reformulated as an integral equation of the second kind respect to, Caputo derivative y order α, 1 < α 2, where solution original problem. Using this reformulation, regularity properties both and its z are studied. Based on information a piecewise polynomial collocation meth...