Existence and uniqueness of a nonlinear term realizing a prescribed blow-up time (Regularity and Singularity for Partial Differential Equations with Conservation Laws)

Abstract

This article is a survey of recent papers ([13, 14]) by the authors on an inverse problem of determining a super-linear, nonlinear term of a simple differential equation from information on blow-up time of solutions to the equation. We expand local and global theory to find its nonlinear term realizing a prescribed blow-up time that is a function of an initial data of the differential equation, as well as, to answer the uniqueness question whether the nonlinear term is unique. Some unpublished results, useful examples, and an overview of main ideas for the proof are also contained.