Results 271 to 280 of about 11,044,020 (324)

Weak Solutions of SDEs

2015
So far, we have focussed on solutions of SDEs where we are simply given a filtration, and with it the Brownian motion W and the random measure μ. We then construct the solution to our equation ( 17.2). In essence, we have used no properties of the filtration except the fact that W and μ are adapted.
Samuel N. Cohen, Robert J. Elliott
openaire   +1 more source

Weak Sharp Solutions of Variational Inequalities

SIAM Journal on Optimization, 1998
Summary: We give sufficient conditions for the finite convergence of descent algorithms for solving variational inequalities involving generalized monotone mappings.
Marcotte, Patrice, Zhu, Daoli
openaire   +1 more source

Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor

Annals of Mathematics, 2015
We prove global existence of appropriate weak solutions for the compressible Navier--Stokes equations for more general stress tensor than those covered by P.-L. Lions and E. Feireisl's theory.
D. Bresch, P. Jabin
semanticscholar   +1 more source

Existence of global weak solutions for 3D degenerate compressible Navier–Stokes equations

, 2015
In this paper, we prove the existence of global weak solutions for 3D compressible Navier–Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins (Commun Math Phys 238:211–223 2003) entropy conservation.
A. Vasseur, Cheng Yu
semanticscholar   +1 more source

Weak Solutions of Forward–Backward SDE's

Stochastic Analysis and Applications, 2003
In this note we study a class of forward–backward stochastic differential equations (FBSDE for short) with functional-type terminal conditions. In the case when the time duration and the coefficients are “compatible” (e.g., the time duration is small), we prove the existence and uniqueness of the strong adapted solution in the usual sense.
ANTONELLI, FABIO, MA J.
openaire   +1 more source

Weak Solutions of Fluid-Solid Interaction Problems

Mathematische Nachrichten, 2000
This paper is concerned with various variational formulations for fluid-solid interaction problems. The basic approach is a coupling of field and boundary integral equation methods. In particular, Gårding's inequalities are established in appropriate Sobolev spaces for all the formulations.
Hsiao, George C., Kleinman, Ralph E., Roach, Gary F.   +2 more
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Extension of weak solutions

1997
Let 0 < T < +∞, A and B be c.n.o. in H. In the previous chapter, we have answered the following question: what must be A and B for each bounded weak solution of equation (1) on [0,T) to have a limit in H as t → T?
openaire   +1 more source

Boundedness of weak solutions

1993
Let u be a weak solution of equations of the type of (1.1) of Chap. II in Ω T We will establish local and global bounds for u in. Ω T . Global bounds depend on the data prescribed on the parabolic boundary of Ω T . Local bounds are given in terms of local integral norms of u. Consider the cubes K ρ ⊂ K 2ρ .
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Regularity of Weak Solutions

1998
It is shown that under appropriate ellipticity assumptions, weak solutions of partial differential equations (PDEs) are smooth. This applies in particular to the Laplace equation for harmonic functions, thereby justifying Dirichlet’s principle introduced in the previous paragraph.
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Weak Solutions for Hyperbolic Equations

2018
In principle, in this chapter, we will study the wave equation, which constitutes the prototype of the hyperbolic equations. Let \(\Omega \) be an open set from \(\mathrm{I}\!\mathrm{R}^n\) and T a real number \(T>0\). Then, the Cauchy problem, associated with the wave equation, consists of $$\begin{aligned}&\frac{\partial ^2u}{\partial t^2}(t,x)- \
Marin Marin, Andreas Öchsner
openaire   +1 more source