| Abstract: |
| We consider dynamics of certain reaction-diffusion equations, which can be interpreted as gradient flows on Banach spaces with a Riemannian structure. It has been shown by F. Otto for the porous media equation, and M. Liero and A. Mielke for diffusion equations with a reaction term, that there are examples of such systems where the entropy functional has positive definite Hessian, or equivalently which satisfy $\lambda$-convexity condition. We give some examples of such systems, and discuss implications to dynamics and stability on bounded and unbounded domains, including diffusive repair. |
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