1,721,040 research outputs found
On the linear Boltzmann equation in evolutionary domains with absorbing boundary
No full textWe consider the linear Boltzmann equation under the effect of an absorbing moving barrier. We prove the existence and uniqueness of the solution and consider the problem of the time-asymptotic convergence to equilibrium. We then propose a numerical strategy to study the problem and provide quantitative results concerning some relevant test cases
The diffusive limit of Carleman-type models in the range of very fast diffusion equations
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On the optimal choice of coefficients in a truncated Wild sum and approximate solutions for the Kac equation
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Optimal estimate of the spectral gap for the degenerate Goldstein-Taylor model
No full textIn this paper we study the decay to the equilibrium state for the solution of a generalized version of the Goldstein-Taylor system, posed in the one-dimensional torus T = R/Z, by allowing that the nonnegative cross section σ can vanish in a subregion X:= {x ∈ T{pipe} σ(x)=0} of the domain with meas (X)≥0 with respect to the Lebesgue measure. We prove that the solution converges in time, with respect to the strong L2-topology, to its unique equilibrium with an exponential rate whenever (T\X)≥0 and we give an optimal estimate of the spectral gap
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