Strongly nonlinear parabolic initial-boundary value problems.

  title={Strongly nonlinear parabolic initial-boundary value problems.},
  author={Ha¨ım Brezis and F E Browder},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  volume={76 1},
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.