Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion
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...
| Main Author: | |
|---|---|
| Format: | Others |
| Language: | English |
| Published: |
Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag
2013
|
| Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22955 |
| id |
ndltd-UPSALLA1-oai-DiVA.org-ntnu-22955 |
|---|---|
| record_format |
oai_dc |
| spelling |
ndltd-UPSALLA1-oai-DiVA.org-ntnu-229552013-10-12T04:37:49ZNonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusionengEndal, JørgenNorges teknisk-naturvitenskapelige universitet, Institutt for matematiske fagInstitutt for matematiske fag2013We 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 $L^{\infty}(\mathbb{R}^d)$ Student thesisinfo:eu-repo/semantics/bachelorThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22955Local ntnudaim:9366application/pdfinfo:eu-repo/semantics/openAccess |
| collection |
NDLTD |
| language |
English |
| format |
Others
|
| sources |
NDLTD |
| description |
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 $L^{\infty}(\mathbb{R}^d)$ |
| author |
Endal, Jørgen |
| spellingShingle |
Endal, Jørgen Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion |
| author_facet |
Endal, Jørgen |
| author_sort |
Endal, Jørgen |
| title |
Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion |
| title_short |
Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion |
| title_full |
Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion |
| title_fullStr |
Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion |
| title_full_unstemmed |
Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion |
| title_sort |
nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion |
| publisher |
Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag |
| publishDate |
2013 |
| url |
http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22955 |
| work_keys_str_mv |
AT endaljørgen nonlinearfractionalconvectiondiffusionequationswithnonlocalandnonlinearfractionaldiffusion |
| _version_ |
1716604524707184640 |