A uniqueness result for a parabolic partial differential equation with hysteresis and convection is established. This equation is a part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The result of this paper complements the content of [6], where existence of the solution has been proved under fairly general assumptio...

Abstract. In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in R. Then we establish an uniform estimate for bubbling solutions of a locally defined Liouville system near an isolated blowup point. The uniqueness result, as well as the local uniform estimates are crucial in...

In this paper, we prove the existence and uniqueness of a coupled best proximity point for mappings satisfying the proximally coupled contraction condition in a complete ordered metric space. Further, our result provides an extension of a result

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

A mixed finite element method combined with a fixed point algorithm is proposed for solving the thermally coupled quasi-Newtonian flow problem. The existence and uniqueness of the mixed variational solution are established. A more general uniqueness result for the original system problem is presented. The convergence of the approximate solution is analyzed and the corresponding error estimates ...

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

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.

In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the ...

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.