Vol. 34, No. 3, 1970

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Local regularity of solutions of Sobolev-Galpern partial differential equations

Ralph Edwin Showalter

Vol. 34 (1970), No. 3, 781–787

Let M and L be elliptic differential operators of orders 2m and 2l, respectively, with m l The existence and uniqueness of a solution to the abstract mixed initial and boundary value problem

M u′(t)+ Lu (t) = 0,u(0) = u0

was established for u0 given in the domain of the infinitesimal generator of a strongly-continuous semi-group. The purpose of this paper is to show that this semi-group is holomorphic and then obtain differentiability results for the solution and convergence of this solution to the initial function u0 as t 0.

Mathematical Subject Classification
Primary: 35.24
Received: 23 October 1969
Published: 1 September 1970
Ralph Edwin Showalter