Record Details
Nonlinear Degenerate Evolution Equations and Partial Differential Equations of Mixed Type
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | Nonlinear Degenerate Evolution Equations and Partial Differential Equations of Mixed Type |
| Names |
Showalter, R. E.
(creator) |
| Date Issued | 1975-02 (iso8601) |
| Note | 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. |
| Abstract | The Cauchy problem for the evolution equation Mu’(t) + N(t,u(t)) = 0 is studied, where M and N(t,•) are, respectively, possibly degenerate and nonlinear monotone operators from a vector space to its dual. Sufficient conditions for existence and for uniqueness of solutions are obtained by reducing the problem to an equivalent one in which M is the identity but each N(t,•) is multivalued and accretive in a Hilbert space. Applications include weak global solutions of boundary value problems with quasilinear partial differential equations of mixed Sobolev-parabolic-elliptic type, boundary conditions with mixed space-time derivatives, and those of the fourth or fifth type. Similar existence and uniqueness results are given for the semilinear and degenerate wave equation Bu"(t) + F(t, u’(t)) + Au(t) = 0, where each nonlinear F(t,•) is monotone and the nonnegative B and positive A are self-adjoint operators from a reflexive Banach space to its dual. |
| Genre | Article |
| Identifier | Showalter, R. E. (1975). Nonlinear degenerate evolution equations and partial differential equations of mixed type. SIAM Journal on Mathematical Analysis, 6(1), 25-42. doi:10.1137/0506004 |
