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On the long time behaviour of solutions to dissipative wave equations in \(\mathbb{R}^{2} \)

  • R. CavazzoniEmail author
Original Paper
  • 31 Downloads

Abstract.

In this paper we present a parabolic approach to studying the diffusive long time behaviour of solutions to the Cauchy problem:
$$ \left\{ \begin{aligned} & u_{{ t t }} + u_{t} - \Delta u = 0,x \in R^{N} ,t \ > 0,\\ & u(\cdot, 0) = u_{0} ,x \in R^{N} ,\\ & u(\cdot, 0) = u_{1} ,x \in R^{N} x; \end{aligned} \right. $$
(1)
where u0 and u1 satisfy suitable assumptions.

After an appropriate scaling we obtain the convergence to a stationary solutio n in L q norm (1 ≤  q  <  ∞).

2000 Mathematics Subject Classification.

35L15 35B40 

Keywords.

Wave equation with linear damping long-time behavior diffusion wave 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Reggio EmiliaITALY

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