Stable time periodic solutions for damped sine-Gordon equations.
Star shaped coincidence sets in the obstacle problem
Statistical Solutions of PDEs by Nonstandard Densities.
Statistically stationary solutions to the 3-D Navier-Stokes equation do not show singularities.
Steady states for a fragmentation equation with size diffusion
The existence of a one-parameter family of stationary solutions to a fragmentation equation with size diffusion is established. The proof combines a fixed point argument and compactness techniques.
Stefan problem in a 2D case
The aim of this paper is to analyze the well posedness of the one-phase quasi-stationary Stefan problem with the Gibbs-Thomson correction in a two-dimensional domain which is a perturbation of the half plane. We show the existence of a unique regular solution for an arbitrary time interval, under suitable smallness assumptions on initial data. The existence is shown in the Besov-Slobodetskiĭ class with sharp regularity in the L₂-framework.
Stefan problems with a concentrated capacity
Vengono brevemente studiati i problemi di Stefan su «capacità concentrate»,seguendo l'approccio recentemente introdotto di G. Savaré e A. Visintin.
Stochastic averaging lemmas for kinetic equations
We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale.Compared to the deterministic case and as far as we work in , the nature of regularity on averages is not changed in this stochastic kinetic equation and stays in the range of fractional Sobolev spaces at the price of an additional expectation. However all the exponents are changed; either time decay rates are slower (when the right...
Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem
Let H be a separable real Hilbert space and let E be a separable real Banach space. We develop a general theory of stochastic convolution of ℒ(H,E)-valued functions with respect to a cylindrical Wiener process with Cameron-Martin space H. This theory is applied to obtain necessary and sufficient conditions for the existence of a weak solution of the stochastic abstract Cauchy problem (ACP) (t∈ [0,T]), almost surely, where A is the generator of a -semigroup of bounded linear operators on...
Stochastic differential equations in Hilbert spaces
Stochastic evolution equations driven by Liouville fractional Brownian motion
Let be a Hilbert space and a Banach space. We set up a theory of stochastic integration of -valued functions with respect to -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter . For we show that a function is stochastically integrable with respect to an -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an -cylindrical fractional Brownian motion. We apply our results to stochastic evolution equations...
Stochastic integration of functions with values in a Banach space
Let H be a separable real Hilbert space and let E be a real Banach space. In this paper we construct a stochastic integral for certain operator-valued functions Φ: (0,T) → ℒ(H,E) with respect to a cylindrical Wiener process . The construction of the integral is given by a series expansion in terms of the stochastic integrals for certain E-valued functions. As a substitute for the Itô isometry we show that the square expectation of the integral equals the radonifying norm of an operator which is...
Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model
Inverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial...
Stochastic methods and differential geometry
Stochastic Navier-Stokes equations with artificial compressibility in random durations.
Stochastic nonlinear Schrödinger equations driven by a fractional noise, well-posedness, large deviations and support.
Stochastic Swift-Hohenberg equation near a change of stability
Stochastic weak attractor for a dissipative Euler equation.
Stokes equations in asymptotically flat layers
We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer . Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded -calculus for the associated Stokes operator and some...
Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations