Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 166, pp. 1-7.
Title: Analytic semigroups generated by an operator matrix in
L^2(Omega) X L^2(Omega)
Author: Salah Badraoui (Univ. du 08 Mai 1945, Guelma, Algeria)
Abstract:
This article concerns the generation of analytic semigroups by an
operator matrix in the space $L^2(\Omega)\times L^2(\Omega)$.
We assume that one of the diagonal elements is strongly elliptic and
the other is weakly elliptic, while the sum of the non-diagonal
elements is weakly elliptic.
Submitted June 15, 2012. Published September 28, 2012.
Math Subject Classifications: 35B40, 35B45, 35K55, 35K65.
Key Words: Analytic semigroup; infinitesimal generator; operator matrix;
dissipative operator; dual space; adjoint operator;
strongly elliptic operator.