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Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Mathematical Sciences.
2013 (English)MasteroppgaveStudent thesis
Abstract [en]

We study nonlinear fractional convection-diffusion equations with nonlocal and nonlinear fractional diffusion. By the idea of Kru\v{z}kov (1970), entropy sub- and supersolutions are defined in order to prove well-posedness under the assumption that the solutions are elements in $L^{\infty}(\mathbb{R}^d\times (0,T))\cap C([0,T];L_\text{loc}^1(\mathbb{R}^d))$. Based on the work of Alibaud (2007) and Cifani and Jakobsen (2011), a local contraction is obtained for this type of equations for a certain class of L\'evy measures. In the end, this leads to an existence proof for initial data in $L^{\infty}(\mathbb{R}^d)$

Place, publisher, year, edition, pages
Institutt for matematiske fag , 2013. , 71 p.
URN: urn:nbn:no:ntnu:diva-22955Local ID: ntnudaim:9366OAI: diva2:655557
Available from: 2013-10-11 Created: 2013-10-11 Last updated: 2013-10-11Bibliographically approved

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