Poches de tourbillon visqueuses
POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems
An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD a-posteriori error estimator developed by Tröltzsch...
POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems∗
An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD...
Poincaré theorem and nonlinear PDE's
A family of formal solutions of some type of nonlinear partial differential equations is found. Terms of such solutions are Laplace transforms of some Laplace distributions. The series of these distributions are locally finite.
Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.
The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal...
Poincaré's inequality and global solutions of a nonlinear parabolic equation
Point fixe d'une application non contractante.
We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.
Point interactions in two diemsions: Basic properties, approximations and applications to solid state physics.
Points critiques dans les problèmes variationnels sans compacité
Pointwise Accuracy of a Finite Element Method for Nonlinear Variational Inequalities.
Pointwise and locally uniform convergence of holomorphic and harmonic functions
We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
Pointwise bounds for solutions of the equation - ...v + pv = 0.
Pointwise bounds on the asymptotics of spherically averaged -solutions of one-body Schrödinger equations
Pointwise controllability as limit of internal controllability for the wave equation in one space dimension.
Pointwise convergence to the initial data for nonlocal dyadic diffusions
We solve the initial value problem for the diffusion induced by dyadic fractional derivative in . First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator....
Pointwise curvature estimates for F-stable hypersurfaces
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation
We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.
Pointwise Error Estimates for a Streamline Diffusion Finite Element Scheme.
Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s
We prove pointwise gradient bounds for entire solutions of pde’s of the form ℒu(x) = ψ(x, u(x), ∇u(x)), where ℒ is an elliptic operator (possibly singular or degenerate). Thus, we obtain some Liouville type rigidity results. Some classical results of J. Serrin are also recovered as particular cases of our approach.