Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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UNIQUENESS RESULTS FOR THE NONLINEAR HYPERBOLIC SYSTEM WITH JUMPING NONLINEARITY

  • Jung, Tack-Sung (Department of Mathematics, Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education, Inha University)
  • Received : 2007.11.22
  • Accepted : 2007.11.28
  • Published : 2007.12.25
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Abstract

We investigate the existence of solutions u(x, t) for a perturbation b[$(\xi+\eta+1)^+-1$] of the hyperbolic system with Dirichlet boundary condition (0.1) = $L\xi-{\mu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$, $L\eta={\nu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$ where $u^+$ = max{u,0}, ${\mu},\nu$ are nonzero constants. Here $\xi,\eta$ are periodic functions.

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References

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