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We show that the gradient flow u on L 2 generated by the energy functional I[u] := U Φ(det Du) dx for vector-valued mappings is in some sense " integrable " , meaning that (i) the inverse Jacobian β := (det Du) −1 satisfies a scalar nonlinear diffusion equation, and (ii) we can recover u by solving an ODE determined by β.

- L C Evans, M Portilheiro
- 2005

Our intention in this paper is to publicize and extend somewhat important work of Plotnikov [P] on the asymptotic limits of solutions of viscous regularizations of an nonlinear diffusion PDE with a cubic nonlinearity. Since the formal limit PDE is in general ill–posed, we expect that the limit solves instead a corresponding diffusion equation with… (More)

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