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Well-Posedness and Regularity for the Wave Equation with Variable Coefficients

Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter, we will consider the initial-boundary value problem for the wave equation on a manifold with boundary . The initial-boundary value problem corresponds to the elliptic operator \(-\varDelta _\mathrm {g}\) introduced in Chap.  2. We will develop a standard approach to prove the existence and uniqueness of solutions and to study their regularity proprieties.

Copyright information

© Springer Japan KK 2017

Authors and Affiliations

  1. 1.Department of MathematicsENIT—LAMSIN, University of Tunis El ManarTunisTunisia
  2. 2.Department of Mathematical SciencesThe University of TokyoTokyoJapan
  3. 3.Research Center of Nonlinear Problems of Mathematical PhysicsPeoples’ Friendship University of RussiaMoscowRussia

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