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Nonautonomous fragmentation equation via evolution semigroups. (English) Zbl 1213.47045

The following Cauchy problem for a nonautonomous multiple-fragmentation equation is treated in this paper:
\[ u_t(t,x)=-a(t,x)u(t,x)+\int_x^\infty a(t,y)b(t,x,y)u(t,y)\,dy, \quad t>s, \text{ a.e. } x>0, \]
with the initial value \(u(s,x)=f(x)\), a.e. \(x>0\). The main tool is the evolution semigroup.

MSC:

47D06 One-parameter semigroups and linear evolution equations
34G10 Linear differential equations in abstract spaces
35R09 Integro-partial differential equations
47A55 Perturbation theory of linear operators
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References:

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