2018
DOI: 10.1112/jlms.12110
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Asymptotic behavior of solutions to fractional diffusion–convection equations

Abstract: We consider a convection–diffusion model with linear fractional diffusion in the sub‐critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective part of the equation. The proof is based on suitable apriori estimates, among which proving an Oleinik type inequality plays a key role.

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Cited by 14 publications
(25 citation statements)
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References 44 publications
(127 reference statements)
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“…Passing to the limit, the same estimate is inherited by U M . A similar tail control argument has been used by one of the authors in [38] for a fractional diffusion-convection equation. III.…”
Section: Existence Of a Rescaled Solutionmentioning
confidence: 98%
“…Passing to the limit, the same estimate is inherited by U M . A similar tail control argument has been used by one of the authors in [38] for a fractional diffusion-convection equation. III.…”
Section: Existence Of a Rescaled Solutionmentioning
confidence: 98%
“…In the purely parabolic case (1.1), the behaviour of the solutions and the underlying theory is different from the convection-diffusion case (especially so in the nonlocal case, see e.g. [30,31,68,29,69] and [42,18,1,22,2,52]). It is therefore important to develop numerical methods and analysis that are specific for this setting.…”
Section: Introductionmentioning
confidence: 98%
“…For convection-diffusion equations, only few cases with special initial or boundary value conditions have analytical solutions. Therefore, most of the main concerns were the study of the qualitative properties of the solutions [5][6][7][8][9][10][11][12][13] and numerical study [14][15][16][17][18][19][20][21][22][23] for convection-diffusion equations. However, the very important approximate solution of convection-diffusion equation has not been well solved.…”
Section: Introductionmentioning
confidence: 99%