Sentence examples for problem for the evolution from inspiring English sources

In this section, we study the Cauchy problem for the evolution equation (1.1).

We close this section by stating and proving that the Cauchy problem for the evolution equation (1.1) is well posed.

The rest of the paper is organized as follows: The Cauchy problem for the evolution equation (1.1) is investigated in Section 2; the approximate controllability of the system (1.1) is established in Section 3; an illustrative example is provided in Section 4 for the main results of this paper; in Section 5 several concluding remarks are presented.

The situation of this paper is that the Stokes equation for the compressible viscous fluid flow in the upper half-space is coupled via inhomogeneous interface conditions with the Stokes equations for the incompressible one in the lower half-space, which is the model problem for the evolution of compressible and incompressible viscous fluid flows with a sharp interface.

This could be a potential problem for the evolution of complexity in prebiotic evolution in addition to the error-threshold.

These investigations are of great importance, both for the problem of the evolution of galaxies and for the study of still-unknown properties of matter.

With the introduction of a signaling component, there are two new complications that could cause problems for the evolution of indirect reciprocity.

In this paper, we investigate how the initial value belonging to spaces (W_{sigma}(mathbb{R}^{N})) ((0for the Cauchy problem of the evolution p-Laplacian equation with absorption.

In future work, we hope to continue to study the properties of solutions for the Cauchy problem of the evolution p-Laplacian equation with the initial value (u_{0}) belonging to other Banach spaces, especially the unbounded spaces.

In this paper we formulate a boundary value problem for the microstructural evolution during a diffusional transformation in a binary alloy.

In [6], Mu and Fan investigate the existence and uniqueness of positive mild solutions of the following periodic boundary value problem for the fractional evolution equations in an ordered Banach space in [6]: left { begin{array}{l} D^{alpha}u(t)+Au(t)=f t,u(t)),quad tin[0,omega], u(0)=u omega), end{array} right.