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Long time asymptotics of fourth order parabolic equations
Journal d'Analyse Mathématique, 1995The development of the spectral properties for parabolic equations associated with higher-order elliptic operators is quite different from the corresponding second-order operators. In particular, the long time behaviour of solutions can be strikingly different from what one is familiar with for second-order ones.
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Long-Time Asymptotics for Integrable Nonlinear Wave Equations
1993We recall the remarkable discovery of Gardner, Green, Kruskal and Miura [9]. Consider the solution of the Korteweg de Vries (KdV) equation $${{q}_{t}} - 6q{{q}_{x}} + {{q}_{{xxx}}} = 0$$ (0.1) with initial data $$q(x,0) = {{q}_{0}}(x) \in \mathcal{S}(R).$$ (0.2)
P. A. Deift, A. R. Its, X. Zhou
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Long-time asymptotics for the asymptotically periodic Korteweg-de Vries equation
2009Wir betrachten eines der bekanntesten Beispiele einer vollständig integrablen nichtlinearen Wellengleichung, die Korteweg-de Vries (KdV) Gleichung. Das Ziel dieser Arbeit ist es das Langzeitverhalten von Lösungen der KdV Gleichung zu untersuchen, die kleine Störungen von (quasi-)periodischen KdV Lösungen darstellen.
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Long–time asymptotics for semiconductor crystals
Nonlinear Analysis: Theory, Methods & Applications, 2001Bechouche, Philippe +2 more
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