Asymptotic behavior of solutions to the short pulse equation with critical nonlinearity

作者：Niizato Tomoyuki^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2014, 111: 15-32.

DOI：10.1016/j.na.2014.08.008

• Short pulse equation
• Scattering problem
• Time decay estimate
• Asymptotic behavior of solutions

We consider the Cauchy problem for the short pulse equation
{u(tx) = u + (u(3))(xx), x is an element of R, t > 0,
u (0, x) = u(0) (x), x is an element of R,
where u(0) is a real valued function. We prove the global existence of small solutions to the short pulse equation. Moreover we give the L-infinity time decay estimate vertical bar vertical bar u(t)vertical bar vertical bar(L infinity) <= C(1 + t)(-1/2) and the asymptotic behavior of solutions.

• 出版日期2014-12