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Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion

Endal, Jørgen
Master thesis
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URI
http://hdl.handle.net/11250/259223
Date
2013
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  • Institutt for matematiske fag [2675]
Abstract
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 $L^{\infty}(\mathbb{R}^d)$
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Institutt for matematiske fag

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