Almost Global Existence of Solutions to the Kadomtsev-Petviashvili Equations

Abstract

We consider the Cauchy problem for the Kadomtsev-Petviashvili equations ut + uxxx + σ∂x–1uyy = –(u2)x, (x, y) ∈ R2, tR, 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.

Journal

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 55 (1), 157-168, 2012

    Division of Functional Equations, The Mathematical Society of Japan

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