论文标题
与潜在消耗模型的趋化性趋化度均匀解决方案的均匀解决方案
Uniform in time solutions for a chemotaxis with potential consumption model
论文作者
论文摘要
在这项工作中，我们在\，$ \ mathbb {r}^n $（$ n = 1,2,3 $）的有限域中研究了以下与消耗模型的化学方法： $$ \ partial_t u-ΔU= - \ nabla \ cdot（u \ nabla v），\ quad \ partial_t v-ΔV= -u^s v $$，其中$ s \ ge 1 $，具有隔离的边界条件和$（u，v）$的初始条件。模型中的主要新颖性是非线性潜在消费术语$ u^sv $。 通过适当截短模型的溶液的收敛，建立了两个主要结果。 $ 3D $域中的时代弱解决方案的存在，以及$ 2D $（或$ 1D $）域中的独特性和规律性。这两个结果都被证明是在域边界上施加最小的规律性假设。
In this work we investigate the following chemo-attraction with consumption model in bounded domains of \, $\mathbb{R}^N$ ($N=1,2,3$): $$ \partial_t u - Δu = - \nabla \cdot (u \nabla v), \quad \partial_t v - Δv = - u^s v $$ where $s\ge 1$, endowed with isolated boundary conditions and initial conditions for $(u,v)$. The main novelty in the model is the nonlinear potential consumption term $u^sv$. Through the convergence of solutions of an adequate truncated model, two main results are established; existence of uniform in time weak solutions in $3D$ domains, and uniqueness and regularity in $2D$ (or $1D$) domains. Both results are proved imposing minimal regularity assumptions on the boundary of the domain.
