In this paper the authors study a nonlinear elliptic-parabolic system, which is motivated by mathematical models for lithium ion batteries. For the reliable and fast numerical solution of the system a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The strategy is justified by an a-priori error estimate for the error between the solution to the coupled system a...

The extended trial function method is utilized in birefringent fibers to generate optical soliton solutions the coupled system that correspond Gerdjikov-Ivanov equation with four-wave mixing terms. approach yields singular and bright solutions, addition extremely important periodic are extracted by taken limit of modulus ellipticity Jacobi’s elliptic function. conditions under which solution ex...

the paper is devoted to the study of brenstien polynomials and development of some new operational matrices of fractional order integrations and derivatives. the operational matrices are used to convert fractional order differential equations to systems of algebraic equations. a simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven infinity Laplacian while second elliptic involves usual Laplacian. We prove that there two-player zero-sum game played in different boards with rules each board (in play Tug-of-War taking number of plays into consideration move at random) whose value functions converge ...

This paper is concerned with the state-constrained optimal control of the threedimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabo...

In this article, we study the existence of positive solutions for the coupled elliptic system −∆u = λ(f(u, v) + h1(x)) in Ω, −∆v = λ(g(u, v) + h2(x)) in Ω, u = v = 0 on ∂Ω, under certain conditions on f, g and allowing h1, h2 to be singular. We also consider the system −∆u = λ(a(x)u+ b(x)v + f1(v) + f2(u)) in Ω, −∆v = λ(b(x)u+ c(x)v + g1(u) + g2(v)) in Ω, u = v = 0 on ∂Ω, and prove a Rabinowitz...

We consider a state-of-the-art ferroelectric phase-field model arising from the engineering area in recent years, which is mathematically formulated as coupled elliptic-parabolic differential system. utilize fixed point theorem based on maximal parabolic regularity theory to show local time well-posedness of problem. The result will firstly be proved under certain general assumptions. then give...