They also examine the connection between the results on the partial differential equation and the well-posedness
of the underlying stochastic/ordinary differential equation.
follows by a standard application of the Lax-Milgram lemma.
So far, Well-posedness
of statistical solutions has been shown only in the case of scalar conservation laws.the main aim of the proposed project is to analyze statistical solutions of systems of conservation laws and incompressible euler equations and to design efficient numerical approximations for them.
In Section 2, we recall the well-posedness
of the problem (1).
For the important case [beta] < 5/4, Wu [8, 9] studied the well-posedness
The next section deals with the well-posedness
of the model and the existence of equilibria.
In particular, we are interested in providing the stability properties of the forms involved (inf-sup conditions, boundedness), at the continuous and discrete level, which are the main requirements to deduce the well-posedness
of (1.1) and its Galerkin scheme and to derive the corresponding error analysis.
In this piece of interesting work, numerical experiments are taken to show the accuracy of PPM in space and its ability to increase the well-posedness
of the inverse problem.
In the next section we investigate the well-posedness
and equilibria for system (2)-(4).
The local well-posedness
of the CSS system in [H.sup.2], [H.sup.1] was shown in [2, 3], respectively.
We prove the well-posedness
of the proposed model and study the effect of delay and cure rate in controlling HIV-1.
We devote Section 2 to a discussion of regularizing properties, including well-posedness
and convergence rate.