An Inverse Piston Problem with Small BV Initial Data

An Inverse Piston Problem with Small BV Initial Data Acta Appl Math https://doi.org/10.1007/s10440-018-0193-y 1,2,3 1,2,3 Libin Wang · Youren Wang Received: 2 September 2017 / Accepted: 19 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In this paper, we consider an inverse piston problem with small BV initial data for the system of one-dimensional adiabatic flow. Suppose that the original state of the gas on the right side of the piston and the position of the forward shock are known, then we can globally solve the inverse piston problem and estimate the speed of the piston in a unique manner. Mathematics Subject Classification (2000) 35L45 · 35L60 · 35R30 Keywords Quasilinear hyperbolic system · Bounded variation norm · Inverse piston problem · One-dimensional adiabatic flow 1 Introduction Suppose that a piston originally located at the origin at t = 0 moves towards the right with the speed v = φ(t) in a straight tube, the length of which is assumed to be infinite. In order to determine the state of the ideal gas on the right side of this piston, in Lagrangian representation this piston problem asks us to solve the following mixed initial-boundary value problem (see [3, 11, 15]): ⎪ ∂ τ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

An Inverse Piston Problem with Small BV Initial Data

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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
D.O.I.
10.1007/s10440-018-0193-y
Publisher site
See Article on Publisher Site

Abstract

Acta Appl Math https://doi.org/10.1007/s10440-018-0193-y 1,2,3 1,2,3 Libin Wang · Youren Wang Received: 2 September 2017 / Accepted: 19 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In this paper, we consider an inverse piston problem with small BV initial data for the system of one-dimensional adiabatic flow. Suppose that the original state of the gas on the right side of the piston and the position of the forward shock are known, then we can globally solve the inverse piston problem and estimate the speed of the piston in a unique manner. Mathematics Subject Classification (2000) 35L45 · 35L60 · 35R30 Keywords Quasilinear hyperbolic system · Bounded variation norm · Inverse piston problem · One-dimensional adiabatic flow 1 Introduction Suppose that a piston originally located at the origin at t = 0 moves towards the right with the speed v = φ(t) in a straight tube, the length of which is assumed to be infinite. In order to determine the state of the ideal gas on the right side of this piston, in Lagrangian representation this piston problem asks us to solve the following mixed initial-boundary value problem (see [3, 11, 15]): ⎪ ∂ τ

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 28, 2018

References

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