Double-phase parabolic equations with variable growth and nonlinear sources

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Double-phase parabolic equations with variable growth and nonlinear sources

Popis výsledku v původním jazyce

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 &lt; p(-) &lt;= p(z) &lt;= q(z) &lt; 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 &lt;= delta &lt; 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 &gt; 0.

Název v anglickém jazyce

Double-phase parabolic equations with variable growth and nonlinear sources

Popis výsledku anglicky

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 &lt; p(-) &lt;= p(z) &lt;= q(z) &lt; 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 &lt;= delta &lt; 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 &gt; 0.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14413Y" target="_blank" >GJ19-14413Y: Lineární a nelineární eliptické rovnice se singulárními daty a související problémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Advances in Nonlinear Analysis

ISSN

2191-9496

e-ISSN

2191-950X

Svazek periodika

12

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

32

Strana od-do

304-335

Kód UT WoS článku

000851222200002

EID výsledku v databázi Scopus

2-s2.0-85138305562