Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations

Some have diffusion and cross-diffusion ecological model

Author LiJianJun
Tutor GaoWenJie
School Jilin University
Course Applied Mathematics
Keywords Eco - Epidemiological Model Prey model Reciprocity model Very few of Positive Stationary Solutions Stability Degree theory Existence Blasting
CLC O175.2
Type PhD thesis
Year 2009
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Application of linear and nonlinear differential equations of population ecology and epidemiology has a very long history , but the epidemic in the ecosystem can not be ignored , so joint epidemiological factors of ecology is necessary , this paper studies two a description of the epidemic spread in prey with homogeneous Neumann boundary condition diffusion equations. then considered two models with cross-diffusion predator , prey model in which cross-diffusion in biological explanation for the Predators chase prey ( prey ) and prey to escape predators. such cross-diffusion phenomena occur in the majority of the ecological environment . Finally a descriptive study of strongly coupled degenerate reciprocal model reaction-diffusion equations and global existence blasting article first use semigroup theory gives two descriptions eco - epidemiological model reaction-diffusion equations dissipative use of topological degree theory proves that the model number of positive stationary solution very existence and differences. found for different reaction function , the diffusion coefficient for very few existence of Positive Stationary Solutions influence is different. then analyzes the diffusion and cross diffusion in two prey model number on the very positive impact of steady-state solution was found that when the no cross-diffusion time constant steady-state solution is a local ( or even global ) asymptotically stable , the incidence of cross-diffusion can produce very few positive stationary solution . Finally, regularization, as estimated , pumping sub- column method to get a description of reciprocity model is strongly coupled reaction-diffusion equations degenerate local existence by comparison with ordinary differential equations obtained positive solutions to the global existence of a condition , while taking advantage of anyway to get reciprocity than competition law , and the two species' habitats adequately the case of large solution of the equations in finite time .

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