Existence And Stability Of Traveling Curved Fronts In Reaction—diffusion Equation With Delay

The theory of traveling wave solutions of parabolic equations is one of the fast developing areas of modern mathematics and has been widely applied to combustion, chemical reactions, nerve propagation, epidemiology and biological models. Due to time delays which usually exist in nature, there have been a number of works devoted to the study of delayed reaction diffusion equations. Because many practical problems from the field of physics, chemistry and ecolo-gy are high-dimensional problems, the study of nonplanar traveling wave solutions of reaction diffusion equations in multidimensional space has attracted much at-tention. Compared with the planar fronts, the nonplanar traveling waves become more complicated. Therefore, it is very meaningful and challengeable to study the nonplanar traveling wave solution of delayed reaction diffusion equations. This thesis is mainly concerned with the existence and stability of nonplanar traveling wave solution for the following delayed reaction diffusion equationFirst of all, we study the existence of traveling curved front of delayed re-action diffusion equations. By constructing a super-and subsolution, we obtain the existence of traveling curved front in Chapter2. Under the assumption con-ditions, there exists a traveling curved fronts v×(x, y+st) satisfying We also show that the traveling curved front is asymptotic stable in Chapter3, if the initial condition satisfy φ(x,y,r)≥v-(x,y+sr), Υ∈[-Υ,0], the solution u(x, y. t;φ) of initial problem satisfy Moreover, we give a dissusion in Chapter to end this thesis.