Of concern are systems of linear evolution equations $$\dot u(t)=\s A u(t),\qquad u(0)=u_0,\leqno({\rm ACP})$$ where $u$ is a function with values in a product Banach space $\s E :=E^n$ and $\s A=(p_{ij}(A))$ is a $n\times n$ matrix whose entries are polynomials in a fixed linear, possibly unbounded operator $A$ on $E$. In this paper we will study the well-posedness of $({\rm ACP})$, i.e., we will characterize those polynomial operator matrices $\s A$ generating a strongly continuous semigroup on $\s E$.
POLYNOMIAL OPERATOR MATRICES AS GENERATORS - THE GENERAL-CASE
ENGEL, KLAUS JOCHEN OTTO
1990-01-01
Abstract
Of concern are systems of linear evolution equations $$\dot u(t)=\s A u(t),\qquad u(0)=u_0,\leqno({\rm ACP})$$ where $u$ is a function with values in a product Banach space $\s E :=E^n$ and $\s A=(p_{ij}(A))$ is a $n\times n$ matrix whose entries are polynomials in a fixed linear, possibly unbounded operator $A$ on $E$. In this paper we will study the well-posedness of $({\rm ACP})$, i.e., we will characterize those polynomial operator matrices $\s A$ generating a strongly continuous semigroup on $\s E$.File in questo prodotto:
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