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- W3100237784 abstract "This paper deals with a boundary-value problem for a coupled quasilinear chemotaxis--haptotaxis model with nonlinear diffusion $$left{begin{array}{ll} u_t=nablacdot(D(u)nabla u)-chinablacdot(unabla v)-xi nablacdot(unabla w)+mu u(1-u-w), v_t=Delta v- v +u,quad w_t=- vw end{array}right. $$ in $N$-dimensional smoothly bounded domains, where the parameters $xi ,chi> 0$, $mu> 0$. The diffusivity $D(u)$ is assumed to satisfy $D(u)geq C_{D}u^{m-1}$ for all $u > 0$ with some $C_D>0$. Relying on a new energy inequality, in this paper, it is proved that under the conditions $$m>frac{2N}{N+{{{frac{(frac{max_{sgeq1}lambda_0^{frac{1}{{{s}}+1}} (chi+xi|w_0|_{L^infty(Omega)})}{(max_{sgeq1}lambda_0^{frac{1}{{{s}}+1}}(chi+xi|w_0|_{L^infty(Omega)})-mu)_{+}}+1) (N+frac{max_{sgeq1}lambda_0^{frac{1}{{{s}}+1}}(chi+xi|w_0|_{L^infty(Omega)})}{(max_{sgeq1}lambda_0^{frac{1}{{{s}}+1}} (chi+xi|w_0|_{L^infty(Omega)})-mu)_{+}}-1)}{N}}}}},$$ and proper regularity hypotheses on the initial data, the corresponding initial-boundary problem possesses at least one global bounded classical solution when $D(0) > 0$ (the case of non-degenerate diffusion), while if, $D(0)geq 0$ (the case of possibly degenerate diffusion), the existence of bounded weak solutions for system is shown. This extends some recent results by several authors." @default.
- W3100237784 created "2020-11-23" @default.
- W3100237784 creator A5077280174 @default.
- W3100237784 date "2020-11-17" @default.
- W3100237784 modified "2023-09-26" @default.
- W3100237784 title "A new result for boundedness of solutions to a quasilinear higher-dimensional chemotaxis -- haptotaxis model with nonlinear diffusion" @default.
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- W3100237784 doi "https://doi.org/10.48550/arxiv.2011.09072" @default.
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