相关论文: Solvability of Coupled Forward-Backward Volterra I…

In this paper, we study backward stochastic Volterra integral equations of type-I with time delayed generators. Under some condition (small time horizon or a Lipschitz constant), we derive an existence and uniqueness results. Next, with the…

This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations, where the solution X^{u,\xi}(t)=X(t) is given by X(t) =\phi(t)+\int_{0}^{t}}b(t,s,X(s),u(s))…

We present a residual-based a posteriori error estimate for the Electric Field Integral Equation (EFIE) on a bounded polyhedron. The EFIE is a variational equation formulated in a negative order Sobolev space on the surface of the…

This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different…

This paper contains a study on stochastic Volterra integral equations with fuzzy sets-values and involving on a constant retardation. Moreover, the form of the equation is symmetric in the sense that fuzzy stochastic integrals are placed on…

We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential…

Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a finite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global $L^2…

This paper addresses a new class of generalized Bolza problems governed by nonconvex integro-differential inclusions with endpoint constraints on trajectories, where the integral terms are given in the general (with time-dependent…

This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…

Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…

Many integral equations used to analyze scattering, such as the standard combined field integral equation (CFIE), are not well-conditioned for a wide range of frequencies and multi-scale geometries. There has been significant effort to…

In this paper, we study the solvability of a class of multi-dimensional forward backward stochastic differential equations (FBSDEs) with oblique reflection and unbounded stopping time. Under some mild assumptions on the coefficients in such…

In this paper, we consider the {\it tensor absolute value equations} (TAVEs), which is a newly introduced problem in the context of multilinear systems. Although the system of TAVEs is an interesting generalization of matrix {\it absolute…

We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic…

The Transport-of-Intensity equation (TIE) has been proven as a standard approach for phase retrieval. Some high efficiency solving methods for the TIE, extensively used in many works, are based on a Fourier-Transform (FT). However, to solve…

We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces

Segregated direct boundary-domain integral equations (BDIEs) based on a parametrix and associated with the Dirichlet and Neumann boundary value problems for the linear stationary diffusion partial differential equation with a variable…

We study in this paper the wellposedness of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-dependent we mean that the coefficients of the forward-backward SDE at time t can depend on the…

We introduce a Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in two spatial variables. PIEs are an algebraic state-space representation of infinite-dimensional systems and have been used to model 1D…