Nabil Merazga

Université Larbi Ben Mhidi · Department of Mathematics and Computer Science

The present paper is devoted to the investigation of a model parabolic mixed problem with boundary integral conditions arising in the context of thermoelasticity. Existence, uniqueness and continuous dependence upon data of a weak solution of the latter are proved by means of the Galerkin method.

In this paper, we deal with a transmission problem for a class of quasilinear pseudoparabolic equations. Existence, uniqueness and continuous dependence of the solution upon the data are obtained via the Rothe method. Moreover, the conver-gence of the method and an error estimate of the approximations are established.

In this paper, we construct a semidiscrete approximate solution to a semilinear one-dimensional heat equation subject to integral boundary conditions by means of the Rothe discretization in time method. The convergence of the approximation scheme obtained is proved, yielding the well-posedness of the problem considered.

In this article, we use the Rothe time-discretization method to prove the well-posedness of a mixed problem with integral conditions for a third order semilinear pseudoparabolic equation. Also we establish the convergence of the method and an error estimate for a semi-discrete approximation.

This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe method which is based on a semidiscretization of the given...

We investigate a model parabolic mixed problem with purely boundary integral conditions arising in the context of thermoelasticity. Using the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable, the questions of existence, uniqueness, and continuous dependence upon data of a weak solution are p...

This paper presents a well-posedness result for an initial-boundary value problem with only integral conditions over the spatial domain for a one-dimensional quasilinear wave equation. The solution and some of its properties are obtained by means of a suitable application of the Rothe time-discretization method.

This paper deals with an initial boundary value problem with an integral condition for the two-dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one-dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are prove...