Well‐posedness,smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics |
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| Authors: | Mark Lichtner Mindaugas Radziunas Lutz Recke |
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| Institution: | 1. Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany;2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany;3. Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, GermanyInstitute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany=== |
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| Abstract: | We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd. |
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| Keywords: | existence uniqueness regularity of weak solutions smooth dependence on data smooth semiflow property existence of smooth invariant centre manifolds non‐autonomous system discontinuous coefficients laser dynamics |
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