Almost Global Existence of Solutions to the Kadomtsev-Petviashvili Equations

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概要

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• We consider the Cauchy problem for the Kadomtsev-Petviashvili equations ut + uxxx + σ∂x–1uyy = –(u2)x, (x, y) ∈ R2, t ∈ R, u(0, x, y) = u0(x, y), (x, y) ∈ R2, where σ = 1 or σ = –1, ∂x–1 = ∫–∞x dx′. We prove that the maximal existence time T is estimated from below as T ≥ exp(C/ε), where ε denotes the size of the initial data, C > 0 is a constant.

著者

• Niizato Tomoyuki

  Osaka University

• Naumkin Pavel

  UNAM

• Hayashi Nakao

  Osaka University

関連論文

• Almost Global Existence of Solutions to the Kadomtsev-Petviashvili Equations
• Asymptotics in Time of Solutions to Nonlinear Schroedinger Equations in Two Space Dimensions
• Large Time Behavior of Small Solutions to Dirichlet Problem for Landau-Ginzburg Type Equations

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