Displaying similar documents to “Time estimates for the Cauchy problem for a third-order hyperbolic equation.”

Existence of Global Solutions to Supercritical Semilinear Wave Equations

Georgiev, V. (1996)

Serdica Mathematical Journal

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∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology. In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was...

Variable depth KdV equations and generalizations to more nonlinear regimes

Samer Israwi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We study here the water waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known that, for such regimes, a generalization of the KdV equation (somehow linked to the Camassa-Holm equation) can be derived and justified [Constantin and Lannes,   (2009) 165–186] when the bottom is flat. We generalize here this result with a new class of equations taking into account variable bottom...