Sentence examples for behavior of large solutions from inspiring English sources

Professor of Mathematics Alexandru Ionescu said, "Yu Deng is not only a brilliant student, he is already an accomplished researcher, whose work has already had significant international impact". Deng plans to conduct further research on global behavior of large solutions including Euler Maxwell and related equations.

In this section, we want to study the behavior of large solutions near the boundary and the uniqueness of the solution.

Later, C Bandle et al. discussed the existence, uniqueness, and accurate estimate of boundary behavior of large solutions for problem (1.1) with (p=2) and (b(x)), (f u)) satisfying some proper conditions and obtained some better results dealing with a gradient term (see [4 40] and the references therein).

It is worth pointing out that Cîrstea and Rǎdulescu [17 19], Cîrstea and Du [20], and Repovs̆ [21] introduced the Karamata regular variation theory to study the boundary behavior and uniqueness of solutions for boundary blow-up elliptic problems and obtained a series of significant information about the qualitative behavior of large solutions in a general framework.

The concern of this paper is the existence, uniqueness, and large-time behavior of classical large solutions to the Cauchy problem (1.1 - 1.3 1.1 - 1.3e vacuum as a far field state, even for the compactly supported density.

The combustion behavior of large scale lithium titanate battery.

We study the local and global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.

Since we are interested in the oscillation and asymptotic behavior of solutions for large t, we assume that (sup mathbb{T}=infty) and define the time scale interval ([t_{0},infty )_{mathbb{T}}) by ([t_{0},infty)_{mathbb{T}}:=[t_{0},infty capmathbb{T}) with (t_{0}inmathbb{T}).

Instead of offering large solutions, the cloud emphasizes small ones.

Based on gradient estimates for the solutions, we classify the behavior of the solutions for large times, obtaining either positivity as t→∞ for q>p−N/(N+1), optimal decay estimates as t→∞ for p/2⩽q⩽p−N/(N+1), or extinction in finite time for 0

Finally, we show how the results in Section 3 can provide information about the behavior of the solutions for large values of t.