Strongly nonlinear parabolic initial-boundary value problems.
An existence and uniqueness result is presented for the solution of a parabolic initial-boundary value problem under Dirichlet null boundary conditions for a general parabolic equation of order 2m with a strongly nonlinear zeroth-order perturbation. This is the parabolic generalization of a class of elliptic results considered earlier by the writers and others and is based upon a new compactness theorem.
Université de Paris VI, Paris 75005, France.
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Brezis
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Browder