Boundedness of solutions to a quasilinear parabolic-parabolic chemotaxis model with variable logistic source
Küçük Resim Yok
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Int Publ Ag
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This 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.
Açıklama
Anahtar Kelimeler
Chemotaxis, Variable logistic source, Global boundedness
Kaynak
Zeitschrift Fur Angewandte Mathematik Und Physik
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
73
Sayı
5
