ON LOCAL SOLVABILITY OF LINEAR EVOLUTIONARY EQUATIONS WITH MEMORY

The authors prove the local unique solvability of the Cauchy problem for linear evolutionary equation with sectorial operator and with integral memory operator in the Banach space. The result is illustrated on the example of the initial boundary value problem for integro-differential equation with partial derivatives.

Keywords

evolutionary equation, integro-differential equation, equation with memory, sectorial operator, analytic semigroup of operators