In this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equation (K (x, t)u’)’ + K(x, t)u’ + A(t)u + F(u) f with null Dirichlet boundary conditions and zero initial data, where F(s) is a continuous function such that sF(s) >_ O, Vs E R and {A(t);t >_ 0} is a family of operators of L(H(2);H-I(gt)) For the existence we appl...

We prove the existence and uniqueness of the mild solution for the 1D Vlasov-Poisson system with initial-boundary conditions by using iterated approximations. The same arguments yield existence and uniqueness for the free space or space periodic system. The major difficulty is the treatment of the boundary conditions. The main idea consists of splitting the velocities range by introducing criti...

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel me...

We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result is established under the general assumption that the diffusion in every fixed environment has a unique non-explosive strong solution. Moreover, non-explosio...

This article outlines the necessary requirements for a coupled system of fractional order boundary value involving Caputo derivative, including its existence, uniqueness, and various forms Ulam stability. We demonstrate existence uniqueness proposed by using cone-type Leray–Schauder result Banach contraction principle. Based on traditional method nonlinear functional analysis, stability is exam...

in this paper we consider the european continuous installment call option. then  its linear complementarity formulation is given. writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. finally finite element method is applied to price the european continuous installment call option.

This paper is devoted to the study of the existence and uniqueness of the invariant measure associated to the transition semigroup of a diffusion process in a bounded open subset of Rn. For this purpose, we investigate first the invariance of a bounded open domain with piecewise smooth boundary showing that such a property holds true under the same conditions that insure the invariance of the c...

This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.