<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>179</id>
    <completedYear>2017</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>419</pageFirst>
    <pageLast>448</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>7</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2017-10-12</completedDate>
    <publishedDate>2017-10-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Neumann boundary feedback stabilization for a nonlinear wave equation: A strict H2-Lyapunov function</title>
    <abstract language="eng">For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H2-Lyapunov function and hence also the H2-norm of the difference between the non-stationary and the stationary state decays exponentially with time.</abstract>
    <parentTitle language="eng">Mathematical Control and Related Fields (MCRF)</parentTitle>
    <identifier type="doi">10.3934/mcrf.2017015</identifier>
    <enrichment key="SubmissionStatus">in press</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <author>Martin Gugat</author>
    <author>Günter Leugering</author>
    <author>Ke Wang</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Boundary feedback control, feedback stabilization, exponential stability, isothermal Euler equations, second-order quasilinear equation, Lyapunov function, stationary state, non-stationary state, gas pipeline.</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A03</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">C03</collection>
  </doc>
</export-example>
