Study of degenerate evolution equations with memory by operator semigroup methods (Q345262)

The authors are concerned with an integro-differential equations with infinite history and difference-type kernel. They reduce the problem to a Cauchy problem with a resolvent \(C_0\) semigroup. This approach enables a detailed discussion of existence and uniqueness results for the original problem in a range of settings. The remainder of the paper explores different problems, giving existence/uniqueness results in each case, and includes discussion of the initial-boundary value problem for the linearised integro-differential Oskolkov system describing the dynamics of Kelvin-Voigt fluids in linear approximation which can be dealt with in this way.