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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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
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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