Author:
Soto John Paolo O.,Lope Jose Ernie C.,Ona Mark Philip F.
Abstract
<abstract><p>Consider the second order nonlinear partial differential equation:</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \partial_t^2 u = F(u, \partial_x u), \quad (t, x) \in \mathbb{C}\times \mathbb{R}. $\end{document} </tex-math></disp-formula></p>
<p>Given small analytic data, Yamane was able to obtain the order of the lifespan of the solution with respect to the smallness parameter $ \varepsilon $. 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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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