RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 2005, Volume 60, Issue 6(366), Pages 21–32 (Mi umn1674)  

This article is cited in 11 scientific papers (total in 11 papers)

Non-local quasi-linear parabolic equations

H. Amann

University of Zurich

Abstract: This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal $L_p$ regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona–Malik equation of image processing.

DOI: https://doi.org/10.4213/rm1674

Full text: PDF file (281 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2005, 60:6, 1021–1033

Bibliographic databases:

UDC: 517.95
MSC: 35K10, 35K22, 58D25, 34G20
Received: 02.10.2005

Citation: H. Amann, “Non-local quasi-linear parabolic equations”, Uspekhi Mat. Nauk, 60:6(366) (2005), 21–32; Russian Math. Surveys, 60:6 (2005), 1021–1033

Citation in format AMSBIB
\Bibitem{Ama05}
\by H.~Amann
\paper Non-local quasi-linear parabolic equations
\jour Uspekhi Mat. Nauk
\yr 2005
\vol 60
\issue 6(366)
\pages 21--32
\mathnet{http://mi.mathnet.ru/umn1674}
\crossref{https://doi.org/10.4213/rm1674}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2215752}
\zmath{https://zbmath.org/?q=an:1160.35300}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2005RuMaS..60.1021A}
\elib{http://elibrary.ru/item.asp?id=25787240}
\transl
\jour Russian Math. Surveys
\yr 2005
\vol 60
\issue 6
\pages 1021--1033
\crossref{https://doi.org/10.1070/RM2005v060n06ABEH004279}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000237188900002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33646417036}


Linking options:
  • http://mi.mathnet.ru/eng/umn1674
  • https://doi.org/10.4213/rm1674
  • http://mi.mathnet.ru/eng/umn/v60/i6/p21

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Latushkin YU., Prüss J., Schnaubelt R., “Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions”, J. Evol. Equ., 6:4 (2006), 537–576  crossref  mathscinet  zmath  isi
    2. Wang Rong-Nian, Li Zhen-Qi, Ding Xiao-Hua, “Nonlocal Cauchy problems for semilinear evolution equations involving almost sectorial operators”, Indian J. Pure Appl. Math., 39:4 (2008), 333–346  mathscinet  zmath  isi
    3. Griepentrog J.A., Recke L., “Local existence, uniqueness and smooth dependence for nonsmooth quasilinear parabolic problems”, J. Evol. Equ., 10:2 (2010), 341–375  crossref  mathscinet  zmath  isi
    4. Dokuchaev N., “Weighted in Time Energy Estimates for Parabolic Equations with Applications to Non-Linear and Non-Local Problems”, Dyn. Partial Differ. Equ., 9:4 (2012), 369–381  crossref  mathscinet  zmath  isi
    5. M. Meyries, J. D. M. Rademacher, E. Siero, “Quasi-Linear Parabolic Reaction-Diffusion Systems: A User's Guide to Well-Posedness, Spectra, and Stability of Travelling Waves”, SIAM J. Appl. Dyn. Syst, 13:1 (2014), 249  crossref  mathscinet  zmath  isi
    6. Jizu Huang, Liqun Cao, “Global Regularity and Multiscale Approach for Thermal Radiation Heat Transfer”, Multiscale Model. Simul, 12:2 (2014), 694  crossref  mathscinet  zmath  isi
    7. Meyries M., Veraar M.C., “Traces and Embeddings of Anisotropic Function Spaces”, Math. Ann., 360:3-4 (2014), 571–606  crossref  mathscinet  zmath  isi
    8. Aata M.L., Jose E.C., Roque M.P., “on the Solvability of a Quasilinear Parabotic Problem With Neumann Boundary Condition”, Sci. Diliman, 28:2 (2016), 65–82  isi
    9. Maltsev V., Pokojovy M., “On a parabolic-hyperbolic filter for multicolor image noise reduction”, Evol. Equ. Control Theory, 5:2 (2016), 251–272  crossref  mathscinet  zmath  isi  elib  scopus
    10. Bogoya M., “On Non-Local Reaction-Diffusion System in a Bounded Domain”, Bound. Value Probl., 2018, 38  crossref  mathscinet  isi
    11. Horstmann D., Meinlschmidt H., Rehberg J., “The Full Keller-Segel Model Is Well-Posed on Nonsmooth Domains”, Nonlinearity, 31:4 (2018), 1560–1592  crossref  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:370
    Full text:163
    References:69
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019