Boundedness of solutions to a quasilinear parabolic-parabolic chemotaxis model with variable logistic source

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dc.contributor.authorAyazoglu, Rabil
dc.contributor.authorAkkoyunlu, Ebubekir
dc.date.accessioned2024-10-04T18:48:26Z
dc.date.available2024-10-04T18:48:26Z
dc.date.issued2022
dc.departmentBayburt Üniversitesien_US
dc.description.abstractThis paper deals with the higher dimension quasilinear parabolic-parabolic chemotaxis model involving a source term of logistic type u(t) = del . (phi(u)del u) - V . (psi(u)del upsilon) + g(x, u), tau upsilon(t) = del upsilon - upsilon + u, in (x, t) is an element of Omega x (0, T), subject to nonnegative initial data and homogeneous Neumann boundary condition, where Omega is a smooth and bounded domain in R-N, N >= 1 and psi, phi, g are smooth, positive functions satisfying nu s(q) <= psi <= chi s(q), phi >= sigma s(p), p,q is an element of R, nu, chi, sigma > 0 when s >= s(0) >1, g(x, s) <= eta s(k(x))-mu s(rn)(x) for s > 0, eta >= 0, mu > 0 constants and g(x, 0) >= 0, x is an element of Omega, where k, m are measurable functions with 0 <= k(-) := ess(x is an element of Omega )infk (x) <= k(x) <= m(+) := ess(x is an element of Omega)sup k(x) < +infinity, 1 < m(-) := ess(x is an element of Omega)infm (x) <= m(x) <= m(+) := ess(x is an element of Omega)sup m(x)< +infinity. We extend the constant exponents k = {0, 1} , m > 1 which in logistic source term g(s) < eta s(k) - mu s(m) for s > 0, eta >= 0 , > 0 as variable exponents k(.) >= 0, m(.) > 1 with k(+) < m(-) . It is proved that if q = m(-) -1 (critical case) with mu properly large that mu > mu(0) for some mu(0) > 0, then there exists a classical solution which is global in time and bounded. Furthermore, if q < m(-) - 1, we prove that the classical solutions to the above system are uniformly in-time-bounded without restriction on mu.en_US
dc.identifier.doi10.1007/s00033-022-01847-0
dc.identifier.issn0044-2275
dc.identifier.issn1420-9039
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-85138314997en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.1007/s00033-022-01847-0
dc.identifier.urihttp://hdl.handle.net/20.500.12403/3055
dc.identifier.volume73en_US
dc.identifier.wosWOS:000854504900001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer Int Publ Agen_US
dc.relation.ispartofZeitschrift Fur Angewandte Mathematik Und Physiken_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectChemotaxisen_US
dc.subjectVariable logistic sourceen_US
dc.subjectGlobal boundednessen_US
dc.titleBoundedness of solutions to a quasilinear parabolic-parabolic chemotaxis model with variable logistic sourceen_US
dc.typeArticleen_US

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