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An Integral Formula Adapted to Different Boundary Conditions for Arbitrarily High-Dimensional Nonlinear Klein–Gordon Equations

In: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

Author

Listed:
  • Xinyuan Wu

    (Nanjing University, Department of Mathematics
    Qufu Normal University, School of Mathematical Sciences)

  • Bin Wang

    (Qufu Normal University, School of Mathematical Sciences)

Abstract

This chapterArbitrarily high-dimensional nonlinear Klein–Gordon equations is concerned with the initial-boundary value problem for arbitrarily high-dimensional Klein–Gordon equations, posed on a bounded domain $$\varOmega \subset \mathbb {R}^d$$ for $$d \ge 1$$ and subject to suitable boundary conditions. We derive and analyse an integral formula which proves to be adapted to different boundary conditions for general Klein–Gordon equations in arbitrarily high-dimensional spaces.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2018. "An Integral Formula Adapted to Different Boundary Conditions for Arbitrarily High-Dimensional Nonlinear Klein–Gordon Equations," Springer Books, in: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, chapter 0, pages 221-250, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-9004-2_9
    DOI: 10.1007/978-981-10-9004-2_9
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