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An application of semigroups of locally Lipschitz operators to Carrier equations with acoustic boundary conditions |
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| Authors: | Yoshikazu Kobayashi |
| Institution: | a Department of Mathematics, Faculty of Science and Engineering, Chuo University, Tokyo 112-8551, Japan b Department of Mathematics, Faculty of Science, Shizuoka University, Shizuoka 422-8529, Japan |
| Abstract: | A generation theorem of semigroups of locally Lipschitz operators on a subset of a real Banach space is given and applied to the problem of the well-posedness of the Carrier equation utt−κ(‖u‖2)Δu+γ|ut|p−1ut=0 in Ω×(0,∞) with acoustic boundary condition, where p>2 and Ω is a bounded domain in an arbitrary dimensional space. |
| Keywords: | Semigroup of locally Lipschitz operators Differential inclusion Dissipativity condition Mild solution Comparison function Maximal solution Acoustic boundary condition |
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