Differential equations with non-densely defined operator coefficients, generating semigroups with singularities. (English) Zbl 1002.34051
Consider the Cauchy problem (\(\ast\)) \(v' + Av = f(t)\), \(0 < t \leq 1\), \(v(0) = v_0\), in a Banach space \(E\) under the condition that the nondensely defined operator \(A\) generates a semigroup with a singularity. The author derives conditions that (\(\ast\)) has a unique solution and applies his result to the equation of thermoconductivity.
Reviewer: Klaus R.Schneider (Berlin)
MSC:
| 34G10 | Linear differential equations in abstract spaces |
References:
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