Diffusion phenomenon in Hilbert spaces and applications

  title={Diffusion phenomenon in Hilbert spaces and applications},
  author={Petronela Radu and Grozdena Todorova and Borislav Yordanov},
Article history: Received 29 December 2010 Revised 19 January 2011 Available online 4 February 2011 We prove an abstract version of the striking diffusion phenomenon that offers a strong connection between the asymptotic behavior of abstract parabolic and dissipative hyperbolic equations. An important aspect of our approach is that we use in a natural way spectral analysis without involving complicated resolvent estimates. Our proof of the diffusion phenomenon does not use the individual… CONTINUE READING
4 Citations
42 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 42 references

Energy decay of solutions for the semilinear dissipative wave equations in an exterior domain

  • R. Ikehata
  • Funkcial. Ekvac. 44
  • 2001
Highly Influential
8 Excerpts

Total energy decay for the wave equation in exterior domains with a dissipation near infinity

  • K. Mochizuki, M. Nakao
  • J. Math. Anal. Appl. 326
  • 2007
Highly Influential
5 Excerpts

An optimal estimate for the difference of solutions of two abstract evolution equations

  • R. Chill, A. Haraux
  • J. Differential Equations 193,
  • 2003
Highly Influential
4 Excerpts

Energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations

  • M. Nakao
  • Math. Z. 238
  • 2001
Highly Influential
5 Excerpts

Decay of solutions of the wave equation with a local degenerate dissipation

  • M. Nakao
  • Israel J. Math., 95
  • 1996
Highly Influential
5 Excerpts

Tai-Ping Liu Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping

  • L. Hsiao
  • Comm. Math. Phys. 143
  • 1992
Highly Influential
5 Excerpts

On the asymptotic behavior of solutions of semi-linear wave equations

  • A. Matsumura
  • Publ. Res. Inst. Math. Sci., Kyoto Univ., 12
  • 1976
Highly Influential
5 Excerpts

Energy decay of solutions to the wave equations with linear dissipation localized near infinity

  • K. Mochizuki, H. Nakazawa
  • Publ. Res. Inst. Math. Sci., 37
  • 2001
Highly Influential
3 Excerpts

Global existence and asymptotic behavior of solutions for quasilinear dissipative plate equation

  • Y. Liu, S. Kawashima
  • DCDS, 29
  • 2011
2 Excerpts

Similar Papers

Loading similar papers…