Sentence examples for smooth solution in from inspiring English sources

"Existing EMR solutions address practice inventory and accounts management, but Klinify is the first to provide a smooth solution in managing patients' medical records without changing the workflow process," said Dr. C Sivathasan, a cardiac surgeon based in Singapore and an early user of Klinify.

According to a priori estimates of the smooth solution in Theorem 3.1, now we are in a position to complete the proof of Theorem 1.1, which is more or less standard.

A method is developed for computing solutions to some class of linear and nonlinear transport equations (hyperbolic partial differential equations with smooth solutions), in any dimension, which exploits Shannon sampling, widely used in information theory and signal processing.

Some new blow-up criteria of smooth solutions in terms of the vorticity and the velocity in a homogenous Besov space are established, respectively.

We show that blow-up of spatial derivatives of smooth solutions in finite time occurs to initial boundary value problems for a class of degenerate parabolic equations.

A logarithmal improved blow-up criterion of smooth solutions in an appropriate homogeneous Besov space was obtained by Wang et al. [11].

Kawashima [14] obtained the global existence of smooth solutions in the two-dimensional case when the initial data are a small perturbation of some given constant state.

It has been shown by Alinhac [21, 22] that the null condition implies global existence of smooth solutions in two space dimensions.

Many results concerning the existence and uniqueness of (weak, strong or smooth) solutions in one dimension can be found in (Chen and Wang [2002], [2003]; Kawashima and Okada [1982]) and the references cited therein.

In this paper, we will adapt the method of Chen et al.[13] to establish the local well-posedness for the incompressible porous media equation (1.1) and to obtain a blow-up criterion of smooth solutions in the framework of Triebel-Lizorkin spaces.

The approach suggested for the solution of this problem is based on the search for the solution with minimal Sobolev's norm (the most smooth solution), which provides, in particular, smooth extension of the solution to the area where no input data is available.