A mathematical model for the dynamics of prion proliferation in the presence of chaperone involving a coupled system consisting of an ordinary differential equation and a partial integro‐differential equation is analyzed. For bounded reaction rates, we prove the existence and uniqueness of positive classical solutions with the help of the theory of evolution system. In the case of unbounded reaction rates, the model is set up into a semilinear evolution equation form in the product Banach space $ℝ\times L_1\left((z_0,\infty );(q+z)dz\right)$ and the existence of a unique positive local mild solution is established by using C₀‐semigroups theory of operators.

中文翻译：

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产物空间中存在伴侣分子时a病毒扩散模型半线性演化方程解的研究

分析了在伴侣存在下of病毒增殖动力学的数学模型，该动力学模型包括一个由常微分方程和部分积分微分方程组成的耦合系统。对于有限的反应速率，我们借助演化系统理论证明了正经典解的存在性和唯一性。在无限制反应速率的情况下，将模型建立为乘积Banach空间中的半线性演化方程形式$ℝ\times {\mathrm{大号}}_{\mathrm{1个}}\left(（{ž}_0，\infty ）;（q+ž）dž\right)$利用算子的C _0-半群理论建立了唯一的正局部温和解的存在性。