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.