On direct and inverse problems for odd-order systems of quasilinear evolution equations

TL;DR

This paper investigates direct and inverse problems for odd-order quasilinear evolution systems, establishing well-posedness under certain conditions and introducing integral overdetermination and control inputs.

Contribution

It provides new results on the well-posedness of inverse problems with nonlinearities, using integral overdetermination and control functions for odd-order quasilinear systems.

Findings

Well-posedness results for inverse problems with nonlinearities

Conditions involving small data or short time intervals

Use of integral overdetermination and controls in problem formulation

Abstract

Direct and inverse initial-boundary problems on a bounded interval for systems of quasilinear evolution equations with general nonlinearities are considered. In the case of inverse problems conditions of integral overdetermination are introduced and right-hand sides of equations of special types are chosen as controls. Results on well-posedness of such problems are established. Assumptions on smallness of the input data or smallness of a time interval are required.