Global classical and weak solutions of the prion proliferation model in the presence of chaperone in a banach space

Kapil Kumar Choudhary; Rajiv Kumar; Rajesh Kumar

doi:10.3934/eect.2021039

Article Contents

2022, Volume 11, Issue 4: 1175-1190. Doi: 10.3934/eect.2021039

This issue Previous Article Existence and general decay of Balakrishnan-Taylor viscoelastic equation with nonlinear frictional damping and logarithmic source term Next Article New criteria for exponential stability in mean square of stochastic functional differential equations with infinite delay

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
^* Corresponding author: Kapil Kumar Choudhary

Received: September 30, 2020

Revised: March 31, 2021

Early access: August 2021

Published: August 2022

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Abstract

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.

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Mathematics Subject Classification: 35R09, 47D06.

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References

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