Entire Solutions Of Two Classes Of Reaction-diffusion Equation In Periodic Media

This thesis mainly studies entire solutions of two classes of reaction-diffusion e-quation in periodic media and its properties. One class is reaction-advection-diffusion equation with ignition type nonlinear term. The other class is nonlocal delay reaction diffusion equation with monostable nonlinearity.In the first chapter, the research background, the status quo and the problems for study of this paper are introduced.In the second chapter, we study a class of reaction-advection-diffusion equation with combustion nonlinearity. Firstly, using the comparison principle, we establish the exponential decay behavior at negative infinity of the pulsating traveling fronts. Then by constructing the suitable super- and sub-solutions, we obtain the existence of the entire solution of the equation.In the third chapter, a class of monostable reaction-diffusion equations with de-layed nonlinearity is investigated in periodic media. Using the features of the monos-table type nonlinear term, we construct a proper super- and sub-solutions, and then combining the comparison principle with the method of the super- and sub-solutions, we establish the entire solution of the equation.