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Optimal energy decay in a one-dimensional wave-heat-wave system

Conference Paper


Abstract


  • Harnessing the abstract power of the celebrated result due to Borichev and Tomilov (Math. Ann. 347:455–478, 2010, no. 2), we study the energy decay in a one-dimensional coupled wave-heat-wave system. We obtain a sharp estimate for the rate of energy decay of classical solutions by first proving a growth bound for the resolvent of the semigroup generator and then applying the asymptotic theory of C0-semigroups. The present article can be naturally thought of as an extension of a recent paper by Batty, Paunonen, and Seifert (J. Evol. Equ. 16:649–664, 2016) which studied a similar wave-heat system via the same theoretical framework.

Publication Date


  • 2020

Citation


  • Ng, A. C. S. (2020). Optimal energy decay in a one-dimensional wave-heat-wave system. In Springer Proceedings in Mathematics and Statistics Vol. 325 (pp. 293-314). doi:10.1007/978-3-030-46079-2_17

Scopus Eid


  • 2-s2.0-85083897054

Web Of Science Accession Number


Start Page


  • 293

End Page


  • 314

Volume


  • 325

Abstract


  • Harnessing the abstract power of the celebrated result due to Borichev and Tomilov (Math. Ann. 347:455–478, 2010, no. 2), we study the energy decay in a one-dimensional coupled wave-heat-wave system. We obtain a sharp estimate for the rate of energy decay of classical solutions by first proving a growth bound for the resolvent of the semigroup generator and then applying the asymptotic theory of C0-semigroups. The present article can be naturally thought of as an extension of a recent paper by Batty, Paunonen, and Seifert (J. Evol. Equ. 16:649–664, 2016) which studied a similar wave-heat system via the same theoretical framework.

Publication Date


  • 2020

Citation


  • Ng, A. C. S. (2020). Optimal energy decay in a one-dimensional wave-heat-wave system. In Springer Proceedings in Mathematics and Statistics Vol. 325 (pp. 293-314). doi:10.1007/978-3-030-46079-2_17

Scopus Eid


  • 2-s2.0-85083897054

Web Of Science Accession Number


Start Page


  • 293

End Page


  • 314

Volume


  • 325