DYNAMICS IN A PARABOLIC-ELLIPTIC CHEMOTAXIS SYSTEM WITH LOGISTIC SOURCE INVOLVING EXPONENTS DEPENDING ON THE SPATIAL VARIABLES

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dc.contributor.authorAyazoglu, Rabil
dc.contributor.authorKadakal, Mahir
dc.contributor.authorAkkoyunlu, Ebubekir
dc.date.accessioned2024-10-04T18:49:33Z
dc.date.available2024-10-04T18:49:33Z
dc.date.issued2024
dc.departmentBayburt Üniversitesien_US
dc.description.abstractWe consider the parabolic-elliptic chemotaxis system with the exponents depending on the spatial variables logistic source and nonlinear signal production: ut = Delta u-chi del (u del upsilon)+f (x, u), (x, t) is an element of Omega x (0, T), 0 = Delta upsilon - upsilon +u(gamma) in a bounded domain Omega subset of R-N (N > 1) with smooth boundary, subject to non negative initial data and homogeneous Neumann boundary conditions, where chi > 0, gamma >= 1 and partial derivative/partial derivative nu denotes the outward normal derivative on partial derivative Omega. The logistic function f fulfilling f (x, s) <= eta s - mu s(alpha(x)+1), eta >= 0, mu > 0 for all s > 0 with f (x, 0) >= 0 for all x is an element of Omega, where alpha : Omega -> [1, infinity) is a measurable function. It is proved that if 1 <= alpha (x) < infinity for all x is an element of Omega such that ess inf(x is an element of Omega) alpha (x) > gamma or ess inf(x is an element of Omega) alpha (x) = gamma with mu > chi, then there exists a nonnegative classical solution (u, upsilon) that is global-in-time and bounded. In addition, under the particular conditions gamma = 1 and f (x, s) = mu (s - s(alpha(x)+1)), if mu is sufficiently large, the global bounded solution (u, upsilon) satisfies IIu (, t) - 1II(L)infinity(Omega) + II upsilon (, t) - 1II(L)infinity(Omega) <= Ce (- k/N+2t) for all t > 0 with k = min{ chi 2/4 , 1/2 } , C > 0. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameter conditions, which improves the known results.en_US
dc.identifier.doi10.3934/dcdsb.2023169
dc.identifier.endpage2122en_US
dc.identifier.issn1531-3492
dc.identifier.issn1553-524X
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-85187376864en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage2110en_US
dc.identifier.urihttps://doi.org/10.3934/dcdsb.2023169
dc.identifier.urihttp://hdl.handle.net/20.500.12403/3203
dc.identifier.volume29en_US
dc.identifier.wosWOS:001086232200001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAmer Inst Mathematical Sciences-Aimsen_US
dc.relation.ispartofDiscrete and Continuous Dynamical Systems-Series Ben_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectChemotaxis systemen_US
dc.subjectsignal productionen_US
dc.subjectexponents depending on the spatial variablesen_US
dc.subjectglobal boundednessen_US
dc.subjectasymptotic behavioren_US
dc.titleDYNAMICS IN A PARABOLIC-ELLIPTIC CHEMOTAXIS SYSTEM WITH LOGISTIC SOURCE INVOLVING EXPONENTS DEPENDING ON THE SPATIAL VARIABLESen_US
dc.typeArticleen_US

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