Forced Waves of Parabolic–Elliptic Keller–Segel Models in Shifting Environments
نویسندگان
چکیده
The current paper is concerned with the forced waves of Keller–Segel chemoattraction systems in shifting environments form, 0.1 $$\begin{aligned} {\left\{ \begin{array}{ll} u_t=u_{xx}-\chi (uv_x)_x +u(r(x-ct)-bu),\quad x\in \mathbb {R}\\ 0=v_{xx}- \nu v+\mu u,\quad {R}, \end{array}\right. } \end{aligned}$$ where $$\chi $$ , b, $$\nu and $$\mu are positive constants, $$c\in {R}$$ resource function r(x) globally Hölder continuous, bounded, $$r^*=\sup _{x\in {\mathbb R}}r(x)>0$$ $$r(\pm \infty ):=\lim _{x\rightarrow \pm }r(x)$$ exist, either $$r(-\infty )<02\chi \mu In case it shown (0.1) has a wave solution connecting $$(\frac{r^*}{b},\frac{\mu }{\nu }\frac{r^*}{b})$$ (0, 0) speed c provided $$c>\frac{\chi r^*}{2\sqrt{\nu }(b-\chi )}- 2\sqrt{\frac{r^*(b-2\chi )}{b-\chi }}$$ sufficiently small $$\lambda _\infty >0$$ generalized principal eigenvalue operator $$u(\cdot )\mapsto u_{xx}(\cdot )+cu_{x}(\cdot )+r(\cdot )u(\cdot on $${\mathbb R}$$ certain sense. Some numerical simulations also carried out. indicate existence solutions some parameter regions which not covered theoretical results, induce several problems to be further studied, provide illustration results.
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ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2021
ISSN: ['1040-7294', '1572-9222']
DOI: https://doi.org/10.1007/s10884-020-09924-6