In this paper an inverse problem is considered for a non coercive partial differential equation, issued from a mass conservation cavitation model for a slightly compressible fluid. The cavitation phenomenon and compressibility take place and are described by the Elrod model. The existence of an optimal solution is proven. Optimality conditions are derived and some numerical results are given.

We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the pro...

nonstandard finite difference schemes for the black-scholes partial differential equation preserving the positivity property are proposed. computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the black-scholes equation. unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.

In many inverse problems a functional of u is given by measurements where u solves a partial differential equation of the type L(p)u + Su = q. Here, q is a known source term and L(p), S are operators with p as unknown parameter of the inverse problem. For the numerical reconstruction of p often the heuristically derived Fréchet derivative R′ of the mapping R : p → ’measurement functional of u’ ...

We consider the inverse problem for identification of the coefficient in an elliptic partial differential equation inside of the unit square D, with overposed boundary data. This problem is not investigated enough in the literature due to lack of results about the uniqueness of the inverse problem. Following the main idea of the so-called Method of Variational Imbedding (MVI), we embed the solu...

The article proposes a method for analyzing the Cauchy problem wide class of evolutionary linear partial differential equations with variable coefficients. By applying (inverse) Fourier transform, original equation is reduced to an integro-differential equation, which can be considered as ordinary in corresponding Banach space. selection this space carried out such way that principle contractio...

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection diffusion reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type inter-particle interactions. Furthermore, we consider a new, asymmetric, single exclusion process, studied elsew...