一类双退化非线性反应扩散方程的全解。

IF 4.1 3区数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2018-01-01 Epub Date: 2018-04-24 DOI:10.1186/s13662-018-1606-y

Rui Yan, Xiaocui Li

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引用次数: 4

摘要

研究一类具有双重退化非线性的反应扩散方程全解的存在性。这里的全部解是存在于所有解的经典解[公式:见文本]。借助于比较定理和上下解法，我们构造了一些完整的解，它们表现为两个具有临界速度的相反的行进前解，从x轴两侧相互移动然后湮灭。此外，我们将存在性定理应用于一种特殊的双简并情形。

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Entire solutions for a reaction-diffusion equation with doubly degenerate nonlinearity.

This paper is concerned with the existence of entire solutions for a reaction-diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all [Formula: see text]. With the aid of the comparison theorem and the sup-sub solutions method, we construct some entire solutions that behave as two opposite traveling front solutions with critical speeds moving towards each other from both sides of x-axis and then annihilating. In addition, we apply the existence theorem to a specially doubly degenerate case.

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.