Complex Singularity Analysis for a nonlinear PDE
| dc.creator | Costin, O. | |
| dc.creator | Tanveer, S. | |
| dc.date | 2006-08-12 | |
| dc.date.accessioned | 2026-07-07T07:21:42Z | |
| dc.date.available | 2026-07-07T07:21:42Z | |
| dc.description | We introduce a method of rigorous analysis of the location and type of complex singularities for nonlinear higher order PDEs as a function of the initial data. The method is applied to determine rigorously the asymptotic structure of singularities of the modified Harry-Dym equation $$ H_t + H_y = - {1/2} H^3 + H^3 H_{yyy} : H(y, 0) = y^{-1/2} $$ for small time at the boundaries of the sector of analyticity. Previous work \cite{CPAM}, \cite{invent03} shows existence, uniqueness and Borel summability of solutions of general PDEs. It is shown that the solution to the above initial value problem is represented convergently by a series in a fractional power of $t$ down to a small annular neighborhood of a singularity of the leading order equation. We deduce that the exact solution has a singularity nearby having, to leading order, the same type. | |
| dc.identifier | https://arxiv.org/abs/math/0608305 | |
| dc.identifier | http://arxiv.org/abs/math/0608305 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115391 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35A05,35A20,34M37 | |
| dc.title | Complex Singularity Analysis for a nonlinear PDE | |
| dc.type | text |