Partial differential equations of Sobolev-Galpern type

Ralph Edwin Showalter

Vol. 31 (1969), No. 3, 787–793

DOI: 10.2140/pjm.1969.31.787

Abstract

A mixed initial and boundary value problem is considered for a partial differential equation of the form Mu_t(x,t) + Lu(x,t) = 0, where M and L are elliptic differential operators of orders 2 m and 2 l, respectively, with m ≦ l. The existence and uniqueness of a strong solution of this equation in H₀^l(G) is proved by semigroup methods.

Mathematical Subject Classification

Primary: 35.79

Milestones

Received: 14 February 1969

Published: 1 December 1969