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| Well-Posedness and Mild Solutions of Second-Order Inhomogeneous Boundary Cauchy Problems |
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| KeyWord:Boundary Cauchy problems, cosine functions, semigroups, operator matrices, wave equations |
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| Abstract: |
| This paper is concerned with a class of second-order inhomogeneous boundary Cauchy problems. By making use of the equivalence to a first-order non-autonomous Cauchy problem, we show the existence and uniqueness of classical solutions. Using cosine operator functions theory, we also prove that these solutions are explicitly given by a variation of constants formula, which is still new for second-order boundary Cauchy problems. An application of wave equations is given to illustrate our results. |
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