Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

summary:This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version

Pendidikan Sekolah Rakyat di Jawa pada Masa Pendudukan Jepang dari Perspektif Buku Pelajaran

Keywords: Pendidikan di Jawa, Pendudukan Jepan

Daily Lessons for a 3 Week Intensive Japanese Course

This paper is designed to provide ideas for daily lesson planning for a three week intensive course. The specific teaching methods are pointed out for most of the material according to the characteristics of the particular items. Realizing the importance of visual aids in foreign language teaching, helpful pictures are included in the text as well as several picture files

Stabilization for small mass in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: balanced case

This paper deals with the problem of the quasilinear parabolic--elliptic--elliptic attraction-repulsion chemotaxis system with q = p and χα −ξγ = 0:  1. u =∇·((u+1)m−1∇u−χu(u+1)p−2∇v+ξu(u+1)q−2∇w), 2. 0=∆v+αu−βv, 3. 0 = ∆w+γu−δw in a bounded domain Ω ⊂ Rn (n ∈ N) with smooth boundary ∂ Ω, where m, p, q ∈ R, χ , ξ , α , β , γ , δ > 0 are constants. In the case that m ̸= 1, p ̸= 2 and q ̸= 2 boundedness and finite-time blow-up have been classified by the sizes of $p, q$ and the sign of χ α − ξ γ (Z. Angew.\ Math.\ Phys.; 2022; 73; 61), where the critical case χ α − ξ γ = 0 has been excluded. The purpose of this paper is to prove boundedness and stabilization in the case χα−ξγ =0