| Abstract: |
| In this talk, I will present cross-diffusion and domain-growth induced pattern formation for reaction-diffusion systems with linear cross-diffusion on evolving domains and surfaces. Our major contribution is that by selecting parameter values from spaces induced by cross-diffusion, domain and surface evolution, patterns emerge only when cross-diffusion and domain growth are present. Such patterns do not exist in the absence of cross-diffusion, domain and surface evolution. In order to compute these cross-diffusion domain-induced parameter spaces, linear stability theory is employed to establish the necessary conditions for domain-growth induced cross-diffusion-driven instability for reaction-diffusion systems with linear cross-diffusion. Model reaction-kinetic parameter values are then identified from parameter spaces induced by cross-diffusion and domain-growth only; these exist outside the classical standard Turing space on stationary domains and surfaces. To exhibit these patterns we employ the surface finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. |
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