I want to apply the semigroup approach of nonautonomous evolution equation for the following wave equation $$u'' - \Delta u + \int\limits_0^t {g(s)} \Delta u(s)ds = 0$$ This problem can be written under the standard form of Cauchy problem $$U' = A(t)U$$ where$$ A(t)=\left( \begin{array}{cc} 0 & 1 \\ \Delta -\int_{0}^{t}g(s)\Delta ds & 0% \end{array}% \right) $$ It is obvious that we can't apply the classical semigroups approach because the operator $A$ in this case depends on $t$. I tried to find some references which talk about these things but I didn't secceed. I want from you some advice or halp. Thank you.
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