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Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth

Bruno Nazaret (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This article is devoted to the study of a perturbation with a viscosity term in an elliptic equation involving the p-Laplacian operator and related to the best contant problem in Sobolev inequalities in the critical case. We prove first that this problem, together with the equation, is stable under this perturbation, assuming some conditions on the datas. In the next section, we show that the zero solution is strongly isolated in some sense, among the space of the solutions. Actually, we end the...

Stationary states and moving planes

Gerhard Ströhmer (2008)

Banach Center Publications

Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.

Statistical estimates for generalized splines

Magnus Egerstedt, Clyde Martin (2003)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.

Statistical Estimates for Generalized Splines

Magnus Egerstedt, Clyde Martin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.

Steady Boussinesq system with mixed boundary conditions including friction conditions

Tujin Kim (2022)

Applications of Mathematics

In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution...

Stick-slip transition capturing by using an adaptive finite element method

Nicolas Roquet, Pierre Saramito (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The numerical modeling of the fully developed Poiseuille flow of a newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...

Currently displaying 281 – 300 of 434