Reduction of reaction diffusion system and asymptotic analysis

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1. For the chemotaxis growth model(1) Existence of a traveling front solution and its stability in a channel domain with Neumann boundary condition by using singular limit analysis(2) Existence of a symmetric stationary solution and its stability in 3 dimensional space by using the reduction system(3) Existence of time global non-negative solution and finite dimensional exponential attractor in the case of singular sensitivity function(4) Instability of the non-negative constant solution and divergence of the dimension of the exponential attractor due to the increases of the chemotaxis effect2. For the adsorbate-induced phase transition model(1) Existence of time global non-negative solution and finite dimensional exponential attractor under periodic boundary condition in a finite segment(2) Existence of time global non-negative solution and finite dimensional exponential attractor under Newmann boundary condition in 2dimensional finite domain with C^2 class boundary or convex domain(3) Existence of the stripe and hexagonal stationary solutions due to the bifurcation from non-negative constant solution in the square domain with Newmann boundary condition3. For the forest kinematic model(1) Introduction of three kinds of omega limit sets and investigation of the basic property of these limit sets