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A class of linear partial neutral functional differential equations with nondense domain. (English) Zbl 0915.35109
The paper deals with the linear neutral differential equations on a Banach space $X$, $${d\over dt} (x(t)- Bx(t- h))= A_0x(t)+ Cx(t- h)+ L(x_t),\quad t\ge 0,\quad x(0)= \varphi\in C_X,$$ where $A_0: D(A_0)\subseteq X\mapsto X$ is a linear operator, $B,C\in{\cal L}(X)$, $L$ is a continuous linear functional from $C_X:= C([-h,0],X)$ into $X, \varphi\in C_X$ and $x_t(\theta)= x(t+ \theta)$, ${-h\le\theta\le 0}$. A variation-of-constants formula is derived allowing transformation of integral solutions of the above problem to solutions of an abstract Volterra integral equation. The authors prove existence and uniqueness results and show that the solutions generate an integrated semigroup.
Reviewer: D.Bainov (Sofia)

MSC:
35R10Partial functional-differential equations
35K40Systems of second-order parabolic equations, general
35R15PDE on infinite-dimensional spaces
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References:
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