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Analytic semigroups generated by an operator matrix in L^2(Omega) X L^2(Omega)Keywords: Analytic semigroup , infinitesimal generator , operator matrix , dissipative operator , dual space , adjoint operator , strongly elliptic operator Abstract: This article concerns the generation of analytic semigroups by an operator matrix in the space $L^2(Omega) imes L^2(Omega)$. 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.
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