# American Institute of Mathematical Sciences

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doi: 10.3934/eect.2021039
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## Global classical and weak solutions of the prion proliferation model in the presence of chaperone in a banach space

 Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Pilani-333031, Rajasthan, India

* Corresponding author: Kapil Kumar Choudhary

Received  October 2020 Revised  April 2021 Early access August 2021

The present work is based on the coupling of prion proliferation system together with chaperone which consists of two ODEs and a partial integro-differential equation. The existence and uniqueness of a positive global classical solution of the system is proved for the bounded degradation rates by the idea of evolution system theory in the state space $\mathbb{R} \times \mathbb{R} \times L_{1}(Z,zdz).$ Moreover, the global weak solutions for unbounded degradation rates are discussed by weak compactness technique.

Citation: Kapil Kumar Choudhary, Rajiv Kumar, Rajesh Kumar. Global classical and weak solutions of the prion proliferation model in the presence of chaperone in a banach space. Evolution Equations & Control Theory, doi: 10.3934/eect.2021039
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