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Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2013

Growth order and blow up points for the parabolic Burger's equation under dynamical boundary conditions

Abstract

We investigate the blow up points of the one-dimensional parabolic Burger's equation ∂ t u = ∂ 2 x u − u∂ x u + u p under a dissipative dynamical boundary condition σ∂ t u + ∂ ν u = 0 for one bump initial data. A numerical example of a solution pertaining exactly two bumps stemming from its initial data is presented. Moreover, we discuss the growth order of the L ∞-norm of the solutions when approaching the blow up time.
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Dates and versions

hal-03617588 , version 1 (23-03-2022)

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Joachim von Below, Gaëlle Pincet Mailly, Jean-François Rault. Growth order and blow up points for the parabolic Burger's equation under dynamical boundary conditions. Discrete and Continuous Dynamical Systems - Series S, 2013, ⟨10.3934/dcdss.2013.6.825⟩. ⟨hal-03617588⟩
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