Matches in SemOpenAlex for { <https://semopenalex.org/work/W2939393313> ?p ?o ?g. }
Showing items 1 to 94 of
94
with 100 items per page.
- W2939393313 abstract "This thesis is mainly devoted to the mathematical analysis of some nonlocal models arising in population dynamics. In general, the study of these models meets with numerous difficulties owing to the lack of compactness and of regularizing effects. In this respect, their analysis requires new tools, both theoretical and qualitative. We present several results in this direction.In the first part, we develop a functional analytic toolbox which allows one to handle some quantities arising in the study of these models. In the first place, we extend the characterization of Sobolev spaces due to Bourgain, Brezis and Mironescu to low regularity function spaces of Besov type. This results in a new theoretical framework that is more adapted to the study of some nonlocal equations of Fisher-KPP type. In the second place, we study the regularity of the restrictions of these functions to hyperplanes. We prove that, for a large class of Besov spaces, a surprising loss of regularity occurs. Moreover, we obtain an optimal characterization of the regularity of these restrictions in terms of spaces of so-called “generalized smoothness”.In the second part, we study qualitative properties of solutions to some nonlocal reaction-diffusion equations set in (possibly) heterogeneous domains. In collaboration with J. Coville, F. Hamel and E. Valdinoci, we consider the case of a perforated domain which consists of the Euclidean space to which a compact set, called an “obstacle”, is removed. When the latter is convex (or close to being convex), we prove that the solutions are necessarily constant. In a joint work with J. Coville, we study in greater detail the influence of the geometry of the obstacle on the classification of the solutions. Using tools of the type of those developed in the first part of this thesis, we construct a family of counterexamples when the obstacle is no longer convex. Lastly, in a work in collaboration with S. Dipierro, we study qualitative properties of solutions to nonlinear elliptic systems in variational form. We establish various monotonicity results in a fairly general setting that covers both local and fractional operators." @default.
- W2939393313 created "2019-04-25" @default.
- W2939393313 creator A5039089857 @default.
- W2939393313 date "2018-09-06" @default.
- W2939393313 modified "2023-09-27" @default.
- W2939393313 title "Analysis of some nonlocal models in population dynamics" @default.
- W2939393313 doi "https://doi.org/10.13130/brasseur-julien_phd2018-09-06" @default.
- W2939393313 hasPublicationYear "2018" @default.
- W2939393313 type Work @default.
- W2939393313 sameAs 2939393313 @default.
- W2939393313 citedByCount "0" @default.
- W2939393313 crossrefType "dissertation" @default.
- W2939393313 hasAuthorship W2939393313A5039089857 @default.
- W2939393313 hasConcept C102634674 @default.
- W2939393313 hasConcept C112680207 @default.
- W2939393313 hasConcept C129782007 @default.
- W2939393313 hasConcept C134306372 @default.
- W2939393313 hasConcept C142730499 @default.
- W2939393313 hasConcept C144024400 @default.
- W2939393313 hasConcept C149923435 @default.
- W2939393313 hasConcept C154945302 @default.
- W2939393313 hasConcept C171250308 @default.
- W2939393313 hasConcept C177264268 @default.
- W2939393313 hasConcept C186450821 @default.
- W2939393313 hasConcept C18648836 @default.
- W2939393313 hasConcept C18903297 @default.
- W2939393313 hasConcept C192562407 @default.
- W2939393313 hasConcept C199360897 @default.
- W2939393313 hasConcept C202444582 @default.
- W2939393313 hasConcept C2524010 @default.
- W2939393313 hasConcept C2777212361 @default.
- W2939393313 hasConcept C2777299769 @default.
- W2939393313 hasConcept C2780841128 @default.
- W2939393313 hasConcept C28826006 @default.
- W2939393313 hasConcept C2908647359 @default.
- W2939393313 hasConcept C33923547 @default.
- W2939393313 hasConcept C36503486 @default.
- W2939393313 hasConcept C41008148 @default.
- W2939393313 hasConcept C86803240 @default.
- W2939393313 hasConcept C99730327 @default.
- W2939393313 hasConceptScore W2939393313C102634674 @default.
- W2939393313 hasConceptScore W2939393313C112680207 @default.
- W2939393313 hasConceptScore W2939393313C129782007 @default.
- W2939393313 hasConceptScore W2939393313C134306372 @default.
- W2939393313 hasConceptScore W2939393313C142730499 @default.
- W2939393313 hasConceptScore W2939393313C144024400 @default.
- W2939393313 hasConceptScore W2939393313C149923435 @default.
- W2939393313 hasConceptScore W2939393313C154945302 @default.
- W2939393313 hasConceptScore W2939393313C171250308 @default.
- W2939393313 hasConceptScore W2939393313C177264268 @default.
- W2939393313 hasConceptScore W2939393313C186450821 @default.
- W2939393313 hasConceptScore W2939393313C18648836 @default.
- W2939393313 hasConceptScore W2939393313C18903297 @default.
- W2939393313 hasConceptScore W2939393313C192562407 @default.
- W2939393313 hasConceptScore W2939393313C199360897 @default.
- W2939393313 hasConceptScore W2939393313C202444582 @default.
- W2939393313 hasConceptScore W2939393313C2524010 @default.
- W2939393313 hasConceptScore W2939393313C2777212361 @default.
- W2939393313 hasConceptScore W2939393313C2777299769 @default.
- W2939393313 hasConceptScore W2939393313C2780841128 @default.
- W2939393313 hasConceptScore W2939393313C28826006 @default.
- W2939393313 hasConceptScore W2939393313C2908647359 @default.
- W2939393313 hasConceptScore W2939393313C33923547 @default.
- W2939393313 hasConceptScore W2939393313C36503486 @default.
- W2939393313 hasConceptScore W2939393313C41008148 @default.
- W2939393313 hasConceptScore W2939393313C86803240 @default.
- W2939393313 hasConceptScore W2939393313C99730327 @default.
- W2939393313 hasLocation W29393933131 @default.
- W2939393313 hasOpenAccess W2939393313 @default.
- W2939393313 hasPrimaryLocation W29393933131 @default.
- W2939393313 hasRelatedWork W1598073837 @default.
- W2939393313 hasRelatedWork W2013091681 @default.
- W2939393313 hasRelatedWork W2023474228 @default.
- W2939393313 hasRelatedWork W2065052269 @default.
- W2939393313 hasRelatedWork W2203970889 @default.
- W2939393313 hasRelatedWork W2217180193 @default.
- W2939393313 hasRelatedWork W2351046358 @default.
- W2939393313 hasRelatedWork W2465441504 @default.
- W2939393313 hasRelatedWork W2508152547 @default.
- W2939393313 hasRelatedWork W2612833018 @default.
- W2939393313 hasRelatedWork W2618144884 @default.
- W2939393313 hasRelatedWork W2891860641 @default.
- W2939393313 hasRelatedWork W2945533637 @default.
- W2939393313 hasRelatedWork W2952682018 @default.
- W2939393313 hasRelatedWork W2964905948 @default.
- W2939393313 hasRelatedWork W3012611392 @default.
- W2939393313 hasRelatedWork W3194745370 @default.
- W2939393313 hasRelatedWork W3200205810 @default.
- W2939393313 hasRelatedWork W3203168443 @default.
- W2939393313 hasRelatedWork W826243479 @default.
- W2939393313 isParatext "false" @default.
- W2939393313 isRetracted "false" @default.
- W2939393313 magId "2939393313" @default.
- W2939393313 workType "dissertation" @default.