Uniqueness of conservative solutions to a one-dimensional general quasilinear wave equation through variational principle
Hong Cai, Geng Chen, Yi Du, Yannan Shen
TL;DR
This paper proves the uniqueness of energy conservative weak solutions to a broad class of one-dimensional quasilinear wave equations using characteristic analysis, applicable to large initial data.
Contribution
It establishes the first large data uniqueness result for conservative solutions of general quasilinear wave equations via a variational approach.
Findings
Uniqueness of energy conservative solutions proven
No restrictions on solution size, large data applicable
Analysis based on characteristics
Abstract
In this paper, we prove the uniqueness of energy conservative Holder continuous weak solution to a general quasilinear wave equation by the analysis of characteristics. This result has no restriction on the size of solutions, i.e. it is a large data result.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Nonlinear Partial Differential Equations