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We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.
In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.
We consider the stabilization of a rotating temperature pulse traveling in a continuous
asymptotic model of many connected chemical reactors organized in a loop with continuously
switching the feed point synchronously with the motion of the pulse solution. We use the
switch velocity as control parameter and design it to follow the pulse: the switch
velocity is updated at every step on-line using the discrepancy between the temperature at
the front...
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