TY  - GEN
TI  - A nonlinear structured population model: Global existence and structural stability of measure-valued solutions
Y1  - 2008///
AV  - public
ID  - heidok8453
KW  - structural stability 
KW  -  Radon measures 
KW  -  population dynamics 
KW  -  structured population model 
KW  -  mutational equations
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/8453/
A1  - Lorenz, Thomas
A1  - Marciniak-Czochra, Anna
A1  - Gwiazda, Piotr
N2  - This paper is devoted to the study of the global existence and structural stability of measure-valued solutions to a nonlinear structured population model given in the form of a nonlocal first-order hyperbolic problem on positive real numbers.  In distinction to previous studies, where the L^1 norm was used, we apply the  flat metric, similar to the Wasserstein W^1 distance. We argue that stability using this metric, in addition to mathematical advantages, is consistent with intuitive understanding of empirical data. Structural stability and the uniqueness of the weak solutions are shown under the assumption about the Lipschitz continuity of the kinetic functions. The stability result is based on the duality formula and the Gronwall-type argument.  Using a framework of mutational equations, existence of solutions to the equations of the model is also shown under weaker assumptions, i.e., without assuming Lipschitz continuity of the kinetic functions.
ER  -