Electron. J. Diff. Equ., Vol. 2012 (2012), No. 166, pp. 1-7.

Analytic semigroups generated by an operator matrix in L^2(Omega)X L^2(Omega)

Salah Badraoui

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.

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Salah Badraoui
Laboratoire LAIG, Université du 08 Mai 1945-Guelma
BP 401, Guelma 24000, Algeria
email: sabadraoui@hotmail.com

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