Inverse problems for nonlinear hyperbolic equations

Gunther Uhlmann; Jian Zhai

doi:10.3934/dcds.2020380

Article Contents

2021, Volume 41, Issue 1: 455-469. Doi: 10.3934/dcds.2020380

This issue Previous Article Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction Next Article A brief and personal history of stochastic partial differential equations

Inverse problems for nonlinear hyperbolic equations

Gunther Uhlmann^1, , and
Jian Zhai^2,

1.
Department of Mathematics, University of Washington, Seattle, WA 98195, USA, Institute for Advanced Study, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China
2.
Institute for Advanced Study, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China

^* Corresponding author: gunther@math.washington.edu
^* Corresponding author: gunther@math.washington.edu

Received: April 2020

Early access: November 2020

Published: January 2021

The first author was partially supported by NSF, a Walker Professorship at UW and a Si-Yuan Professorship at IAS, HKUST

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Abstract

There has been considerable progress in recent years in solving inverse problems for nonlinear hyperbolic equations. One of the striking aspects of these developments is the use of nonlinearity to get new information, which is not possible for the corresponding linear equations. We illustrate this for several examples including Einstein equations and the equations of nonlinear elasticity among others.

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Mathematics Subject Classification: Primary:35R30;Secondary:35A27, 35L70.

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