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Journal Articles Acta Applicandae Mathematicae Year : 2013

Convergence of time dependent Turing structure to a stationary solution

Abstract

Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written for the L 2 norm of the solution. This method is appropriate for the equations with time dependent coefficients. It yields new results and is applicable when the usual linearization method is not applicable.

Dates and versions

hal-00846571 , version 1 (19-07-2013)

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Vitaly Volpert, A.G. Ramm. Convergence of time dependent Turing structure to a stationary solution. Acta Applicandae Mathematicae, 2013, 123 (1), pp.31-42. ⟨10.1007/s10440-012-9711-5⟩. ⟨hal-00846571⟩
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