id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-399	Liu, Changchun; Li, Pingping	Boundedness and global solvability for a chemotaxis-haptotaxis model with p-Laplacian diffusion	2020	16	.pdf	application/pdf	5601	222	80	p−2 2 |∇uε|2dx + χmk(mk − 1) ∫ Ω umk−1 ε (1 + uε) −α∇uε∇vεdx + ξmk(mk − 1) ∫ Ω ∇ (∫ uε 0 smk−1(1 + s)−βds ) · ∇wεdx + ∫ Ω µmku mk ε (1− uε − wε)dx. (2.48) EJDE-2020/16 BOUNDEDNESS AND GLOBAL SOLVABILITY 11 It is not difficult to check that mk − 1 ≥ 1 if k ≥ 1 according to (2.41), (2.42) and (2.43). Introduction In this article, we study the problem ut = div(|∇u|p−2∇u)− χ∇ · ( u (1 + u)α ∇v ) − ξ∇ · ( u (1 + u)β ∇w ) + µu(1− u− w), x ∈ Ω, t > 0, vt −∆v + v = f(u)g(w), x ∈ Ω, t > 0, wt = −vw, x ∈ Ω, t > 0, (|∇u|p−2∇u− χ u (1 + u)α ∇v − ξ u (1 + u)β ∇w) · ~n|∂Ω = ∂v ∂~n ∣∣ ∂Ω = 0, u(x, 0) = u0(x), v(x, 0) = v0(x), w(x, 0) = w0(x), x ∈ Ω, (1.1) where Ω is a bounded domain in R3 with the smooth boundary, p > 2, χ, ξ ≥ 0, µ > 0, α > 0, β ≥ 0, f and g satisfy |f(s)| ≤ K1|s|q1 +K2, |g(s)| ≤ K3|s|q2 +K4, 0 < q1 ≤ 1, 0 < q2 <∞, (1.2) with some positive constants Ki.	cache/ejde-399.pdf	txt/ejde-399.txt