Global existence for a class of highly degenerate parabolic systems
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We consider a system of differential equations describing diffusion in polymers. By means of techniques from semigroup theory we prove that it possesses a unique global smooth solution, thus settling some questions, which came up in numerical investigations of this model. From the mathematical point of view the interest in this problem lies in the fact, that it is a degenerate parabolic (2 × 2)-system, whose “diffusion matrix” has rank one only.
Key wordssemilinear parabolic equations analytic semigroups degenerate problems global existence
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