Sentence examples for limits of solutions from inspiring English sources

We consider the limits of solutions of the regularization obtained by decreasing the critical exponent.

The conditions are imposed on the left and right limits of solutions and their derivatives at the interior points and are often called 'transmission conditions' or 'interface conditions.' Such type problems often arise in varies physical transfer problems (see [13]).

We study a class Mp of measures and the corresponding class of non-linear variational μ-capacities, which are closely related to the study of limits of solutions of non-linear Dirichlet problems in open sets with holes.

In the study of equations of mathematical physics, the attractor is a proper mathematical concept as regards the depiction of the behavior of the solutions of these equations when time is large or tends to infinity, which describes all the possible limits of solutions.

It is a problem for future investigation to find values of positive limits of solutions considered in the paper (e.g., by methods used in [25 27]) or to enlarge the presented method to more general classes of equations and initial functions.

The investigation of the inviscid limit of solutions of the Navier-Stokes equations is a classical issue.

In this paper we identify and analyze the phenomena of concentration and cavitation by studying the vanishing pressure limit of solutions of the full Euler equations for nonisentropic compressible fluids with a scaled pressure.

Usually this principle identifies the physically relevant solution as a limit of solutions with some dissipation, namely u t + f u x = ε β u u x x. (2.6).

end{aligned}In particular, the solution u x, t) can be obtained (see [12, 33]) as a limit of solutions (u_{eta })((eta longrightarrow 0^)) of the Cauchy problem begin{aligned} left{ begin{array}{ll} u_{t}= Delta u^{m}&quad text{ in }~Q, u x,0)=u_{0}(x)+eta &quad text{ on }~mathbb {R}^{n}, end{array} right.

The solutions are in fact given as limits of smooth solutions of appropriate approximate equations and we may assume for our estimates that the solutions under consideration are sufficiently smooth.

Owing to the size limit of solution NMR spectroscopy, the number of suitable membrane-mimetic systems is restricted.