Double-phase parabolic equations with variable growth and nonlinear sources
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134048" target="_blank" >RIV/00216224:14310/23:00134048 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/anona-2022-0271" target="_blank" >https://doi.org/10.1515/anona-2022-0271</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/anona-2022-0271" target="_blank" >10.1515/anona-2022-0271</a>
Alternative languages
Result language
angličtina
Original language name
Double-phase parabolic equations with variable growth and nonlinear sources
Original language description
We study the homogeneous Dirichlet problem for the parabolic equations u(t) - div(A(z, vertical bar del u vertical bar)del u) = F(z, u, del u), z = (x, t) is an element of Omega x (0, T), with the double phase flux A(z, vertical bar del u vertical bar)del u (vertical bar del u vertical bar(p(z)-2) + a(z)vertical bar del u vertical bar(q(z) -2))del u and the nonlinear source F. The initial function belongs to a Musielak-Orlicz space defined by the flux. The functions a, p, and q are Lipschitz-continuous, a(z) is nonnegative, and may vanish on a set of nonzero measure. The exponents p, and q satisfy the balance conditions 2N/N+2 < p(-) <= p(z) <= q(z) < p(z) + r*/2 with r* = r* (p(-), N) p(-) = min((Q) over barT) p(z). It is shown that under suitable conditions on the growth of F(z, u, del u) with respect to the second and third arguments, the problem has a solution u with the following properties: u(t) is an element of L-2(Q(T)), vertical bar del u vertical bar(p(z)+delta) is an element of L-1(Q(T)) for every 0 <= delta < r*, vertical bar del u vertical bar(s(z)), a(z)vertical bar del u vertical bar(q(z)) is an element of L-infinity(0, T; L-1(Omega)) with s(z) = max{2, p(z)}. Uniqueness is proven under stronger assumptions on the source F. The same results are established for the equations with the regularized flux A(z, (epsilon(2) + vertical bar del u vertical bar(2))(1/2))del u, epsilon > 0.
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/GJ19-14413Y" target="_blank" >GJ19-14413Y: Linear and nonlinear elliptic equations with singular data and related problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Nonlinear Analysis
ISSN
2191-9496
e-ISSN
2191-950X
Volume of the periodical
12
Issue of the periodical within the volume
1
Country of publishing house
PL - POLAND
Number of pages
32
Pages from-to
304-335
UT code for WoS article
000851222200002
EID of the result in the Scopus database
2-s2.0-85138305562