dc.contributor.author | del Teso, Félix | |
dc.contributor.author | Endal, Jørgen | |
dc.contributor.author | Jakobsen, Espen Robstad | |
dc.date.accessioned | 2019-03-28T08:24:58Z | |
dc.date.available | 2019-03-28T08:24:58Z | |
dc.date.created | 2018-12-17T11:37:46Z | |
dc.date.issued | 2018 | |
dc.identifier.isbn | 978-3-03719-186-6 | |
dc.identifier.uri | http://hdl.handle.net/11250/2592081 | |
dc.description.abstract | We study well-posedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form ∂tu − Aϕ(u) = 0. These equations are possibly degenerate nonlinear diffusion equations with a general nondecreasing continuous nonlinearity ϕ and the largest class of linear symmetric nonlocal diffusion operators A considered so far. The operators are defined from a bilinear energy form E and may be degenerate and have some x-dependence. The fractional Laplacian, symmetric finite differences, and any generator of symmetric pure jump Lévy processes are included. The main results are (i) an Ole˘ınik type uniqueness result for energy solutions; (ii) an existence (and uniqueness) result for distributional solutions with finite energy; and (iii) equivalence between the two notions of solution, and as a consequence, new well-posedness results for both notions of solutions. We also obtain quantitative energy and related L p -estimates for distributional solutions. Our uniqueness results are given for a class of functions defined from test functions by completion in a certain topology. We study rigorously several cases where this space coincides with standard function spaces. In particular, for operators comparable to fractional Laplacians, we show that this space is a parabolic homogeneous fractional Sobolev space. | nb_NO |
dc.language.iso | eng | nb_NO |
dc.publisher | European Mathematical Society Publishing House | nb_NO |
dc.relation.ispartof | Non-linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume | |
dc.title | On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type | nb_NO |
dc.type | Chapter | nb_NO |
dc.description.version | acceptedVersion | nb_NO |
dc.source.pagenumber | 129-168 | nb_NO |
dc.identifier.doi | 10.4171/186-1/7 | |
dc.identifier.cristin | 1644045 | |
dc.relation.project | Norges forskningsråd: 250070 | nb_NO |
dc.description.localcode | This chapter will not be available due to copyright restrictions (c) 2018 by European Mathematical Society Publishing House | nb_NO |
cristin.unitcode | 194,63,15,0 | |
cristin.unitname | Institutt for matematiske fag | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |