Asymptotic analysis of solutions to parabolic systems |
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| Authors: | Vladimir Kozlov Mikael Langer Peter Rand |
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| Institution: | 1. Department of Mathematics, Link?ping University, SE–581 83 Link?ping, Sweden;2. Phone: +46 13 28 24 44, Fax: +46 13 10 07 46;3. Phone: +46 586 73 33 21, Fax: +46 586 73 30 28 |
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| Abstract: | We study asymptotics as t → ∞ of solutions to a linear, parabolic system of equations with time‐dependent coefficients in Ω × (0, ∞), where Ω is a bounded domain. On ? Ω × (0, ∞) we prescribe the homogeneous Dirichlet boundary condition. For large values of t, the coefficients in the elliptic part are close to time‐independent coefficients in an integral sense which is described by a certain function κ (t). This includes in particular situations when the coefficients may take different values on different parts of Ω and the boundaries between them can move with t but stabilize as t → ∞. The main result is an asymptotic representation of solutions for large t. As a corollary, it is proved that if κ ∈ L1(0, ∞), then the solution behaves asymptotically as the solution to a parabolic system with time‐independent coefficients (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Asymptotic behaviour parabolic system Cauchy problem |
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