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Optimal stability
estimates and a new uniqueness result for advection-diffusion
equations
Víctor Navarro-Fernández, André Schlichting and Christian Seis |
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Vol. 4 (2022), No. 3, 571–596
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Abstract |
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We present two main contributions. First, we provide optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev regular in the spatial variable. This estimate is formulated with the help of Kantorovich–Rubinstein distances with logarithmic cost functions. Second, we extend the stability estimates to the advection-diffusion equations with velocity fields whose gradients are singular integrals of functions entailing a new well-posedness result. |
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Keywords
advection-diffusion equation, stability estimates,
uniqueness, Kantorovich–Rubinstein distance
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Mathematical Subject Classification
Primary: 35B30, 35B35, 35B45
Secondary: 35K15
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Milestones
Received: 11 March 2022
Revised: 12 July 2022
Accepted: 6 September 2022
Published: 4 December 2022
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Authors |
| Víctor Navarro-Fernández | |
| Institut für Analysis und
Numerik Westfälische Wilhelms-Universität Münster Münster Germany |
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| André Schlichting | |
| Institut für Analysis und
Numerik Westfälische Wilhelms-Universität Münster Münster Germany |
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| Christian Seis | |
| Institut für Analysis und
Numerik Westfälische Wilhelms-Universität Münster Münster Germany |
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