@article{Soto2024, 
author = {John Paolo O. Soto and Jose Ernie C. Lope and Mark Philip F. Ona},
title = {Lifespan of solutions to second order Cauchy problems with small Gevrey data},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {1434-1442},
keywords = {Cauchy problem, lifespan of solutions, Gevrey functions, small data},
url = {https://www.sciopen.com/article/10.3934/math.2024070},
doi = {10.3934/math.2024070},
abstract = {Consider the second order nonlinear partial differential equation:         ∂    t    2    u  =  F  (  u  ,      ∂    x    u  )  ,    (  t  ,  x  )  ∈      C    ×      R    .Given small analytic data, Yamane was able to obtain the order of the lifespan of the solution with respect to the smallness parameter    ε. On the other hand, Gourdin and Mechab studied the lifespan of the solution given small Gevrey data, but under the assumption that    F is independent of    u. In this paper, we considered non-vanishing Gevrey data and used the method of successive approximations to obtain a solution and constructively estimate its lifespan.}
}