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An extended variational theory for nonlinear evolution equations via modular spaces

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F21%3A43902765" target="_blank" >RIV/60076658:12510/21:43902765 - isvavai.cz</a>

  • Alternative codes found

    RIV/62690094:18470/21:50018547

  • Result on the web

    <a href="https://epubs.siam.org/doi/10.1137/20M1385251" target="_blank" >https://epubs.siam.org/doi/10.1137/20M1385251</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1137/20M1385251" target="_blank" >10.1137/20M1385251</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    An extended variational theory for nonlinear evolution equations via modular spaces

  • Original language description

    We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly nonreflexive and nonseparable spaces. The pivoting point is to establish a novel variational structure, based on abstract modular spaces associated to a given convex function. First, we show that the new variational triple is suited for framing the evolution, in the sense that a novel duality pairing can be introduced and a generalized computational chain rule holds. Second, we prove well-posedness in an extended variational sense for evolution equations, without relying on any reflexivity assumption and any polynomial requirement on the nonlinearity. Finally, we discuss several important applications that can be addressed in this framework: these cover, but are not limited to, equations in Musielak-Orlicz-Sobolev spaces, such as variable exponent, Orlicz, weighted Lebesgue, and double-phase spaces.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    <a href="/en/project/GJ20-19018Y" target="_blank" >GJ20-19018Y: Delicate analytical and topological tools for variational problems and modelling</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    SIAM Journal on Mathematical Analysis

  • ISSN

    0036-1410

  • e-ISSN

  • Volume of the periodical

    53

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    43

  • Pages from-to

    4865-4907

  • UT code for WoS article

    000692288300038

  • EID of the result in the Scopus database

    2-s2.0-85114743215