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Existence of Travelling Waves with Strong Generic Kernel in a Vector-Disease Model

Author: ShaoMingZhe
Tutor: PengYaHong
School: Donghua University
Course: Applied Mathematics
Keywords: Traveling wave solutions Nonlocal delays Geometric singular perturbation theory Epidemic Model
CLC: O175
Type: Master's thesis
Year: 2011
Downloads: 61
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Abstract


Since the seventies of the last world until the 21st century , the traveling wave solutions of reaction-diffusion equations theory has been fully developed. With the application of the theory of traveling wave solutions in a wide range of physical , chemical , biological and other fields , the contents of its existence, uniqueness and stability in-depth research . Time lag must exist in nature , so to get attention from the theory of traveling wave solutions since there is a lot of work from the the starting power systems and semigroup view , delayed reaction diffusion equation . And , since the 1990s , people in the study found delayed reaction diffusion equations can accurately describe some phenomenon of change . In this paper, the existence of traveling wave solutions for a class of infectious diseases diffusion model . In the first chapter introduced the background of the model , current research and some prior knowledge . First, in the second chapter briefly describes the geometric singular perturbation theory and Fredholm theorem . In the subsequent one , considering the situation with a strong generated Delay nuclear first infectious disease model equations into the corresponding traveling wave solutions for the problem , next traveling wave equation into ordinary differential system . Lemma 2.2.1 by proving the existence of links the two equilibrium point heteroclinic orbit . Through the use of geometric singular perturbation theory and the theory of dynamical systems , Fredholm theory invariant manifold theory , prove a sufficiently small time delay , the existence of such Epidemic Model traveling wave solutions of nonlocal delays . In the third chapter , the paper traveling wave solutions of reaction-diffusion equation with delay proved the existence . Establish a relationship on the existence of traveling wave solutions of reaction-diffusion equations with distributed delays between the Reaction Diffusion equation and the existence of consistent non- time delay . Invariant manifold theory , and then use geometric singular perturbation theory , and the theory of dynamical systems and implicit function theorem final conclusion .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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