论文标题
通用Newell-Whitehead-Segel方程的一般解决方案
General Solution For Generalised Newell-Whitehead-Segel Equations
论文作者
论文摘要
在这一专着中，研究了两组抛物线微分方程，每个方程都有非线性培养基响应。这些方程通常称为“ Newell-Whitehead-Segel方程”，该方程模拟了多种非线性物理，机械和生物系统。可以从许多角度看待非线性培养基响应，例如，介质的记忆响应，介质“记住”早期影响。反应性反应，该介质对输入有积极响应，例如化学反应性，湍流和许多其他情况；这些方程式在生物科学中通常会出现在对种群动力学建模时，无论人群是基因组，例如，等位基因还是环境中的动物物种；最后，这些方程组通常被用来对可激发细胞培养基的神经系统反应进行建模。实际上，提供的解决方案具有非常笼统的性质，因此，为一类非线性抛物线偏微分方程提供了一组规范的解决方案，其非线性培养基响应表示为P-Times迭代卷积或P-Times多数响应。规范解决方案集的优点是这些解决方案涉及经典的代表性形式，例如Green的功能或Green的热内核以及帮助研究人员进一步并发症，分析和理解这些类型的非线性系统的系统性行为。
In this monograph, two sets of parabolic differential equations are studied, each with nonlinear medium response. The equations are generally referred to as "Newell-Whitehead-Segel equation," which model a wide variety of nonlinear physical, mechanical and biological systems. Nonlinear medium response can be viewed in many perspectives, such as, memory response from the medium, whereby, the medium "remembers" earlier influences; reactive responses, whereby, the medium is actively responsive to input, such as, chemical reactivity, turbulence and many other circumstances; these equations arise often in the biological sciences when modeling population dynamics, whether the population be genomic, such as, alleles, or animal species in the environment; finally, these sets of equations are often employed to model neurological responses from excitable cellular media. The solutions provided are of a very general nature, indeed, whereby, a canonical set of solutions are given for a class of nonlinear parabolic partial differential equations with nonlinear medium response expressed as either a p-times iterative convolution or p-times multiplicative response. The advantage of canonical solution sets are these solutions involve classic representative forms, such as, Green's function or Green's heat kernel and aid researchers in further complication, analysis and understanding of the systemic behavior of these types of nonlinear systems.
