one of the important subject is the legal status of great dowry; if it is a designated property, the agreement is valid because there is not any limitation on the dowry and spouses can fix it at any amount they may wish in accordance with article 1089 of code civil. if is a general nature property and the husband has the power to deliver it, the agreement is valid but if he has not the power, t...

Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optimal control are proved, as well as necessary optimality conditions. Mathematics ...

We study the question of approximability for the inverse of the FEM stiffness matrix for (scalar) second order elliptic boundary value problems by blockwise low rank matrices such as those given by the H-matrix format introduced by Hackbusch (Computing 62(2):89–108, 1999). We show that exponential convergence in the local block rank r can be achieved. We also show that exponentially accurate LU...

We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for...

The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar’s constraint qualification holds. In this paper, we prove the maximal monotonicity of A+B provided that A,B are maximally monotone and A is a linear relation, as soon as Rockafellar’s constraint qualification holds: domA ∩ int domB 6...