Matches in SemOpenAlex for { <https://semopenalex.org/work/W2963922454> ?p ?o ?g. }
- W2963922454 endingPage "4553" @default.
- W2963922454 startingPage "4537" @default.
- W2963922454 abstract "We investigate the long-time behavior of weak solutions to the thin-film type equation$$v_t =(xv - vv_{xxx})_x ,$$which arises in the Hele-Shaw problem. We estimate the rate of convergence of solutions tothe Smyth-Hill equilibrium solution, which has the form $frac{1}{24}(C^2-x^2)^2_+$, in the norm$$|!|!| f |!|!|_{m,1}^2 = int_{mathbb{R}}(1+ |x|^{2m})|f(x)|^2 , dx + int_{mathbb{R}}|f_x(x)|^2 , dx.$$We obtain exponential convergence in the $|!|!| cdot |!|!|_{m,1}$ norm for all $m$ with $1leq m< 2$, thus obtaining rates of convergence in norms measuring both smoothness and localization. The localization is the main novelty, and in fact, we show that there is a closeconnection between the localization bounds and the smoothness bounds: Convergence of second moments implies convergence in the$H^1$ Sobolev norm. We then use methods of optimal mass transportation to obtain the convergence of the required moments.We also use such methods to construct an appropriate class of weak solutions for which all of the estimates on which our convergence analysis depends may be rigorously derived. Though our main results on convergence can be stated without reference to optimal mass transportation,essential use of this theory is made throughout our analysis." @default.
- W2963922454 created "2019-07-30" @default.
- W2963922454 creator A5047053035 @default.
- W2963922454 creator A5077320234 @default.
- W2963922454 date "2014-05-01" @default.
- W2963922454 modified "2023-10-17" @default.
- W2963922454 title "Localization, smoothness, and convergence to equilibrium for a thin film equation" @default.
- W2963922454 cites W1982159830 @default.
- W2963922454 cites W2008990623 @default.
- W2963922454 cites W2017596211 @default.
- W2963922454 cites W2018371111 @default.
- W2963922454 cites W2032254325 @default.
- W2963922454 cites W2038145626 @default.
- W2963922454 cites W2039498090 @default.
- W2963922454 cites W2041880402 @default.
- W2963922454 cites W2044163325 @default.
- W2963922454 cites W2047530428 @default.
- W2963922454 cites W2049585229 @default.
- W2963922454 cites W2054723044 @default.
- W2963922454 cites W2055054359 @default.
- W2963922454 cites W2058436955 @default.
- W2963922454 cites W2071048859 @default.
- W2963922454 cites W2082979270 @default.
- W2963922454 cites W2083250674 @default.
- W2963922454 cites W2089964069 @default.
- W2963922454 cites W2103743484 @default.
- W2963922454 cites W2122036088 @default.
- W2963922454 cites W2127674094 @default.
- W2963922454 cites W2132883347 @default.
- W2963922454 cites W2501937791 @default.
- W2963922454 cites W2963547883 @default.
- W2963922454 doi "https://doi.org/10.3934/dcds.2014.34.4537" @default.
- W2963922454 hasPublicationYear "2014" @default.
- W2963922454 type Work @default.
- W2963922454 sameAs 2963922454 @default.
- W2963922454 citedByCount "12" @default.
- W2963922454 countsByYear W29639224542016 @default.
- W2963922454 countsByYear W29639224542017 @default.
- W2963922454 countsByYear W29639224542018 @default.
- W2963922454 countsByYear W29639224542019 @default.
- W2963922454 countsByYear W29639224542020 @default.
- W2963922454 countsByYear W29639224542021 @default.
- W2963922454 countsByYear W29639224542022 @default.
- W2963922454 countsByYear W29639224542023 @default.
- W2963922454 crossrefType "journal-article" @default.
- W2963922454 hasAuthorship W2963922454A5047053035 @default.
- W2963922454 hasAuthorship W2963922454A5077320234 @default.
- W2963922454 hasBestOaLocation W29639224541 @default.
- W2963922454 hasConcept C102634674 @default.
- W2963922454 hasConcept C114614502 @default.
- W2963922454 hasConcept C127162648 @default.
- W2963922454 hasConcept C134306372 @default.
- W2963922454 hasConcept C146324458 @default.
- W2963922454 hasConcept C151376022 @default.
- W2963922454 hasConcept C157709441 @default.
- W2963922454 hasConcept C162324750 @default.
- W2963922454 hasConcept C17744445 @default.
- W2963922454 hasConcept C191795146 @default.
- W2963922454 hasConcept C199539241 @default.
- W2963922454 hasConcept C2776257435 @default.
- W2963922454 hasConcept C2777303404 @default.
- W2963922454 hasConcept C28826006 @default.
- W2963922454 hasConcept C2993719964 @default.
- W2963922454 hasConcept C31258907 @default.
- W2963922454 hasConcept C33923547 @default.
- W2963922454 hasConcept C41008148 @default.
- W2963922454 hasConcept C50522688 @default.
- W2963922454 hasConcept C539828613 @default.
- W2963922454 hasConcept C57869625 @default.
- W2963922454 hasConcept C5871375 @default.
- W2963922454 hasConcept C99730327 @default.
- W2963922454 hasConceptScore W2963922454C102634674 @default.
- W2963922454 hasConceptScore W2963922454C114614502 @default.
- W2963922454 hasConceptScore W2963922454C127162648 @default.
- W2963922454 hasConceptScore W2963922454C134306372 @default.
- W2963922454 hasConceptScore W2963922454C146324458 @default.
- W2963922454 hasConceptScore W2963922454C151376022 @default.
- W2963922454 hasConceptScore W2963922454C157709441 @default.
- W2963922454 hasConceptScore W2963922454C162324750 @default.
- W2963922454 hasConceptScore W2963922454C17744445 @default.
- W2963922454 hasConceptScore W2963922454C191795146 @default.
- W2963922454 hasConceptScore W2963922454C199539241 @default.
- W2963922454 hasConceptScore W2963922454C2776257435 @default.
- W2963922454 hasConceptScore W2963922454C2777303404 @default.
- W2963922454 hasConceptScore W2963922454C28826006 @default.
- W2963922454 hasConceptScore W2963922454C2993719964 @default.
- W2963922454 hasConceptScore W2963922454C31258907 @default.
- W2963922454 hasConceptScore W2963922454C33923547 @default.
- W2963922454 hasConceptScore W2963922454C41008148 @default.
- W2963922454 hasConceptScore W2963922454C50522688 @default.
- W2963922454 hasConceptScore W2963922454C539828613 @default.
- W2963922454 hasConceptScore W2963922454C57869625 @default.
- W2963922454 hasConceptScore W2963922454C5871375 @default.
- W2963922454 hasConceptScore W2963922454C99730327 @default.
- W2963922454 hasIssue "11" @default.
- W2963922454 hasLocation W29639224541 @default.
- W2963922454 hasLocation W29639224542 @default.
- W2963922454 hasLocation W29639224543 @default.