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Study of the solution of a semilinear evolution equation of a prion proliferation model in the presence of chaperone in a product space
Author(s) -
Kumar Rajiv,
Choudhary Kapil Kumar,
Kumar Rajesh
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6894
Subject(s) - uniqueness , mathematics , evolution equation , bounded function , ordinary differential equation , partial differential equation , banach space , heat equation , parabolic partial differential equation , mathematical analysis , differential equation , pure mathematics
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 × L 1( z 0 , ∞ ) ; ( q + z ) d zand the existence of a unique positive local mild solution is established by using C 0 ‐semigroups theory of operators.