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Global solvability and stabilization to a cancer invasion model with remodelling of ECM
Nonlinearity ( IF 1.7 ) Pub Date : 2020-08-23 , DOI: 10.1088/1361-6544/ab9249
Chunhua Jin

In this paper, we deal with the Chaplain–Lolas’s model of cancer invasion with tissue remodelling ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5049/nonab9249ieqn1.gif] {$\left\{\begin{aligned}\hfill & {u}_{t}={\Delta}u-\chi \mathbf{\nabla }\cdot \left(u\mathbf{\nabla }v\right)-\xi \mathbf{\nabla }\cdot \left(u\mathbf{\nabla }w\right)+\mu u\left(1-u\right)+\beta uv,\hfill \\ \hfill & {v}_{t}=D{\Delta}v+u-uv,\hfill \\ \hfill & {w}_{t}=-\delta vw+\eta w\left(1-w\right).\hfill \end{aligned}\right.$} We consider this problem in a bounded domain ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5049/nonab9249ieqn2.gif] {${\Omega}\subset {\mathbb{R}}^{N}$} ( N = 2, 3) with zero-flux boundary conditions. We first establish the global existence and uniform boundedness of solutions. Subsequently, we also consider the large time behaviour of solutions, and show that the global classical solution ( u , v ,...

中文翻译:

通过ECM重构,可整体解决癌症模型的稳定性和稳定性

在本文中,我们通过组织重构处理了Chaplain-Lolas的癌症侵袭模型## IMG ## [http://ej.iop.org/images/0951-7715/33/10/5049/nonab9249ieqn1.gif] {$ \ left \ {\ begin {aligned} \ hfill&{u} _ {t} = {\ Delta} u- \ chi \ mathbf {\ nabla} \ cdot \ left(u \ mathbf {\ nabla} v \ right)-\ xi \ mathbf {\ nabla} \ cdot \ left(u \ mathbf {\ nabla} w \ right)+ \ mu u \ left(1-u \ right)+ \ beta uv,\ hfill \\ \ hfill&{v} _ {t} = D {\ Delta} v + u-uv,\ hfill \\ \ hfill&{w} _ {t} =-\ delta vw + \ eta w \ left(1-w \正确)。\ hfill \ end {aligned} \ right。$}我们在有界域中考虑此问题## IMG ## [http://ej.iop.org/images/0951-7715/33/10/5049 /nonab9249ieqn2.gif] {$ {\ Omega} \ subset {\ mathbb {R}} ^ {N} $}(N = 2,3),且零通量边界条件。我们首先建立解决方案的全局存在性和有界界。后来,
更新日期:2020-08-24
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