Nonlinear Degenerate Evolution Equations and Partial Differential Equations of Mixed Type

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Abstract
This is the publisher’s final pdf. The published article is copyrighted by the Society for Industrial and Applied Mathematics and can be found at: http://epubs.siam.org/loi/sjmaah.The Cauchy problem for the evolution equation Mu’(t) + N(t,u(t)) = 0 is studied,ud where M and N(t,•) are, respectively, possibly degenerate and nonlinear monotone operators from aud vector space to its dual. Sufficient conditions for existence and for uniqueness of solutions are obtainedud by reducing the problem to an equivalent one in which M is the identity but each N(t,•) isud multivalued and accretive in a Hilbert space. Applications include weak global solutions of boundaryud value problems with quasilinear partial differential equations of mixed Sobolev-parabolic-ellipticud type, boundary conditions with mixed space-time derivatives, and those of the fourth or fifth type.ud Similar existence and uniqueness results are given for the semilinear and degenerate wave equationud Bu"(t) + F(t, u’(t)) + Au(t) = 0, where each nonlinear F(t,•) is monotone and the nonnegative B andud positive A are self-adjoint operators from a reflexive Banach space to its dual

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