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Description: |
We consider a coupled nonlinear PDE model for image restoration. Both image and edge variables are incorporated by coupling them into two different PDEs. The features of our problem which oppose strong and classical weak well-posedness are the presence of a nonlinear function (modulus) of the image gradient in the right-hand side of the second equation and the Perona-Malik-like form of the diffusion function in the first equation. We show that the Dirichlet initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. This is a joint work with V.B. Surya Prasath.
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