Abstract
In this paper, we establish with suitable assumptions the analyticity of semigroups generated by a pair of generalized mixed linear regular differential operators
L((n;n))u(x) := (L(1n)u(1)(x), L(2n)u(2)(x))
= (Sigma(0 <=kappa <= n) p(k)(x) (d/dx)(k) u(1)(x), Sigma(0 <=kappa <= n) qk(x) (d/dx)(k) u(2)(x))
with involving an interface condition in the setting of complex Hilbert space X = L-2([a, b]) x L-2([b, c]). We obtain quite general results that extend previous works by the authors ([3], [10]). The key for showing the generation analytic semigroups will be an inequality of the form
Re <(L-(n,L-n) - rho I) u, u >(X) + delta vertical bar Im <(L-(n,L-n) - rho I)u, u >(X)vertical bar <= 0, for all u is an element of D(L-(n,L-n))
for some constant rho > 0.