Non-instantaneous single- and multi-impulsive advection-diffusion-reaction equations

Non-instantaneous single- and multi-impulsive advection-diffusion-reaction equations

In the present article, we study singular limits of weak energy solutions to non-instantaneous single-and multi-impulsive advection-diffusion-reaction equation as impulsive source terms collapse to time-dependent the Dirac delta-functions, i.e., to instant impulses. We establish that the limiting fu...

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Veröffentlicht in:AIP Conference Proceedings 2022-09, Vol.2528 (1)
Hauptverfasser: Kuznetsov, Ivan, Sazhenkov, Sergey
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Sprache:eng
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Advection
Diffusion
Glaciology
Impulses
Reaction-diffusion equations
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description In the present article, we study singular limits of weak energy solutions to non-instantaneous single-and multi-impulsive advection-diffusion-reaction equation as impulsive source terms collapse to time-dependent the Dirac delta-functions, i.e., to instant impulses. We establish that the limiting functions are the solutions of the instantaneous impulsive advection-diffusion-reaction equations. Besides, in the multi-impulsive case we find the effect of transition to an equilibrium as a number of impulses grows infinitely. The results can be applied to further modeling of such processes as frost-quakes in glaciology.
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subjects Advection
Diffusion
Glaciology
Impulses
Reaction-diffusion equations
title Non-instantaneous single- and multi-impulsive advection-diffusion-reaction equations
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