论文标题
在存在营养的情况下，应力调制的生长 - 一个空间维度的存在和独特性
Stress-modulated growth in the presence of nutrients -- existence and uniqueness in one spatial dimension
论文作者
论文摘要
在一个空间维度中证明了一类压力调节生长模型的解决方案的存在和独特性。该模型以弹性部分$ f_e $和与增长有关的部分$ g $的变形梯度$ f $的乘法分解为特征。在由于增长过程而受到$ g $管辖的转换之后，应用了$ f_e $描述的弹性变形，以恢复dirichlet边界条件，因此当前配置可能会用压力张量$ s $强调。参考配置中每个点的材料的生长是由右侧的普通微分方程给出的，右侧可能取决于应力$ s $和当前配置中养分浓度的下拉，从而导致了普通微分方程的耦合系统。
Existence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of the deformation gradient $F$ into an elastic part $F_e$ and a growth-related part $G$. After the transformation due to the growth process, governed by $G$, an elastic deformation described by $F_e$ is applied in order to restore the Dirichlet boundary conditions and therefore the current configuration might be stressed with a stress tensor $S$. The growth of the material at each point in the reference configuration is given by an ordinary differential equation for which the right-hand side may depend on the stress $S$ and the pull-back of a nutrient concentration in the current configuration, leading to a coupled system of ordinary differential equations.
