Details
| Original language | English |
|---|---|
| Pages (from-to) | 580-603 |
| Number of pages | 24 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 324 |
| Issue number | 1 |
| Publication status | Published - 1 Dec 2006 |
| Externally published | Yes |
Abstract
We show that a model describing the interaction between normal and infectious prion proteins admits global solutions. More precisely, supposing the involved degradation rates to be bounded, we prove global existence and uniqueness of classical solutions. Based on this existence theory, we provide sufficient conditions for the existence of global weak solutions in the case of unbounded splitting rates. Moreover, we prove global stability of the disease-free steady state.
Keywords
- Asymptotic behavior, Classical and weak solutions, Fragmentation, Global existence, Prion proliferation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of Mathematical Analysis and Applications, Vol. 324, No. 1, 01.12.2006, p. 580-603.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the solvability of a mathematical model for prion proliferation
AU - Simonett, Gieri
AU - Walker, Christoph
N1 - Copyright: Copyright 2006 Elsevier B.V., All rights reserved.
PY - 2006/12/1
Y1 - 2006/12/1
N2 - We show that a model describing the interaction between normal and infectious prion proteins admits global solutions. More precisely, supposing the involved degradation rates to be bounded, we prove global existence and uniqueness of classical solutions. Based on this existence theory, we provide sufficient conditions for the existence of global weak solutions in the case of unbounded splitting rates. Moreover, we prove global stability of the disease-free steady state.
AB - We show that a model describing the interaction between normal and infectious prion proteins admits global solutions. More precisely, supposing the involved degradation rates to be bounded, we prove global existence and uniqueness of classical solutions. Based on this existence theory, we provide sufficient conditions for the existence of global weak solutions in the case of unbounded splitting rates. Moreover, we prove global stability of the disease-free steady state.
KW - Asymptotic behavior
KW - Classical and weak solutions
KW - Fragmentation
KW - Global existence
KW - Prion proliferation
UR - http://www.scopus.com/inward/record.url?scp=33748901876&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2005.12.036
DO - 10.1016/j.jmaa.2005.12.036
M3 - Article
AN - SCOPUS:33748901876
VL - 324
SP - 580
EP - 603
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -