Results 231 to 240 of about 2,506,197 (280)
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Weak Sharp Solutions of Variational Inequalities
SIAM Journal on Optimization, 1998Summary: We give sufficient conditions for the finite convergence of descent algorithms for solving variational inequalities involving generalized monotone mappings.
Marcotte, Patrice, Zhu, Daoli
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Weak Solutions of Forward–Backward SDE's
Stochastic Analysis and Applications, 2003In 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.
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Weak Solutions of Fluid-Solid Interaction Problems
Mathematische Nachrichten, 2000This 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. +2 more
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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?
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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?
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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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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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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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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
2018In 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
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