Stability of constant equilibrium state for dissipative balance laws system with a convex entropy
抄録
<p>For a one-dimensional system of dissipative balance laws endowed with a convex entropy, we prove, under natural assumptions, that a constant equilibrium state is asymptotically<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared"><mml:semantics><mml:mrow class="MJX-TeXAtom-ORD"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:annotation encoding="application/x-tex">{L^2}</mml:annotation></mml:semantics></mml:math></inline-formula>-stable under a zero-mass initial disturbance. The technique is based on the construction of an appropriate Liapunov functional involving the entropy and a so-called compensation term.</p>
収録刊行物
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- Quarterly of Applied Mathematics
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Quarterly of Applied Mathematics 62 (1), 163-179, 2004
American Mathematical Society (AMS)