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On a doubly damped quasilinear wave equation

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Summary

We prove global existence, uniqueness, and asymptotic decay of solutions for an initial and boundary value problem for the equation

$$u_{tt} - u_{xx} - \frac{\partial }{{\partial x}}\beta (u_{xt} ) + f(u_t ) = g(x,t),(x,t) \in (0,1) \times R^ + ,$$

with Β′ possibly degenerate andf not necessary monotone or Lipschitzian, assuming a smallness condition on the initial data and on the forcing term g.

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Hai, D.D. On a doubly damped quasilinear wave equation. Annali di Matematica pura ed applicata 160, 77–87 (1991). https://doi.org/10.1007/BF01764121

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Keywords

  • Initial Data
  • Wave Equation
  • Global Existence
  • Force Term
  • Smallness Condition