Development of reaction-diffusion systems - Studies of singular limit methods -

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Reaction-diffusion systems have been encountered in many fields of natural sciences. In this project, we develop singular limit procedures and comtempolarily numerical methods in order to investigate dynamics of patterns, forms, interfaces and singularities in such systems. In the below, we show our results obtained in this project:(1) Derivation of a free boundary problem from competition-diffusion systems by using singular limit procedures(2) Qualitative study of spiky solutions in biological systems by singular limit procedures.(3) Stability analysis of skew-gradient reaction-diffusion systems.(4) Interaction of traveling pulses and spots by using dynamical system theory(5) Traveling wave solutions of reaction diffusion systems by using singular perturbation methods(6) analysis of motion of mean curvatures in higher dimensional spaces.(7) Analysis of aggregating patterns in diffusion-chemotaxis systems(8) Numerical simulations of complex spatio-temporal patterns in reaction-diffusion systems(9) Development of adoptive FEM methods to reaction-diffusion systems