Local exact controllability of the age-dependent population dynamics with diffusion.
Local exact controllability of the diffusion equation in one dimension.
Local exact controllability to the trajectories of the Boussinesq system
Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.
Local exact lagrangian controllability of the Burgers viscous equation
Local Exchange Potentials for Electronic Structure Calculations
The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized effective...
Local existence and estimations for a semilinear wave equation in two dimension space
In this paper we prove a local existence theorem for a Cauchy problem associated to a semi linear wave equation with an exponential nonlinearity in two dimension space. In this problem, the first Cauchy data is equal to zero, the second is in , radially symmetric and compactly supported. To prove this theorem, we first show a Moser-Trudinger type inequality for the linear problem and then we use a fixed point method to achieve the proof of the result.
Local Existence and Regularity for a Class of Degenerate Parabolic Equations.
Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow.
Local existence in time of small solutions to the Davey-Stewartson systems
Local existence of a solution of a semi-linear wave equation in a neighborhood of initial characteristic hypersurfaces
Local existence of classical solutions to the well-posed Hele-Shaw problem.
Local existence of solutions for an aggregation equation in Besov spaces
We prove the local in time existence of solutions for an aggregation equation in Besov spaces. The Fourier localization technique and Littlewood-Paley theory are the main tools used in the proof.
Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids
The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.
Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids
Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.
Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic compressible fluid
Local existence of solutions for the equations describing the motion of a magnetohydrodynamic compressible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linearized equations is proved, next by the method of successive aproximations local existence to the nonlinear problem is shown....
Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid
Local existence of solutions is proved for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surface. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linarized equations is proved; next by the method of successive aproximations the local existence is shown for the nonlinear problem....
Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method...
Local Existence of Weak Solutions to the Quasi-Linear Wave Equation for Large Initial Values.
Local existence result of the single dopant diffusion including cluster reactions of high order.