On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping

By Felipe Linares, Ademir Fernando Pazoto. 2007

64 citations recorded by the source corpus.

This paper is concerned with the asymptotic behavior of solutions of the critical generalized Korteweg-de Vries equation in a bounded interval with a localized damping term. Combining multiplier techniques and compactness arguments it is shown that the problem of exponential decay of the energy is reduced to prove the unique continuation property of weak solutions. A locally uniform stabilization result is derived.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f6a27023f42e9d64959b25aa5f25f656e6ed9053

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In Control and Systems Engineering

1. R. A. Capistrano–Filho
2. G. Doronin
3. Fágner D. Araruna

In Mathematical Physics

1. R. A. Capistrano–Filho
2. Fágner D. Araruna
3. G. Doronin

In Statistical and Nonlinear Physics

1. R. A. Capistrano–Filho
2. Fágner D. Araruna
3. G. Doronin

Citations in the corpus

• Energy decay for the modified Kawahara equation posed in a bounded domain (2012, background): “For the critical exponent, p = 4, the global well-posedness and the exponential stability were studied in [21].”