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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Second order parabolic equations in Banach spaces with dynamic boundary conditions
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by Ti-Jun Xiao and Jin Liang PDF
Trans. Amer. Math. Soc. 356 (2004), 4787-4809 Request permission

Abstract:

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.
References
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Additional Information
  • Ti-Jun Xiao
  • Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China – and – Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany
  • MR Author ID: 269685
  • Email: xiaotj@ustc.edu.cn, tixi@fa.uni-tuebingen.de
  • Jin Liang
  • Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China – and – Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany
  • MR Author ID: 238393
  • Email: jliang@ustc.edu.cn, jili@fa.uni-tuebingen.de
  • Received by editor(s): June 24, 2002
  • Published electronically: June 25, 2004
  • Additional Notes: The first author acknowledges support from the Alexander-von-Humboldt Foundation and from CAS and NSFC. The second author acknowledges support from the Max-Planck Society and from CAS and EMC
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 4787-4809
  • MSC (2000): Primary 34G10, 47D06, 35G10
  • DOI: https://doi.org/10.1090/S0002-9947-04-03704-3
  • MathSciNet review: 2084398