TY  - INPR
A1  - Kloeden, Peter E.
A1  - Sonner, Stefanie
A1  - Surulescu, Christina
T1  - A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor
N2  - A nonlocal stochastic model for intra- and extracellular proton dynamics in a tumor is proposed. 
The intracellular dynamics is governed by an SDE coupled to a reaction-diffusion 
equation for the extracellular proton concentration on the macroscale. In a more general context  
the existence and uniqueness of solutions for local and nonlocal 
SDE-PDE systems are established allowing, in particular, to analyze the proton dynamics model both,
in its local version and the case with nonlocal path dependence.
Numerical simulations are performed 
to illustrate the behavior of solutions, providing some insights into the effects of randomness on tumor acidity.
KW  - multiscale model
KW  - intra- and extracellular proton dynamics
KW  - tumor acidity
KW  - stochastic differential equations
KW  - partial differential equations
KW  - nonlocal sample dependence
Y1  - 2015
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4104
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-41040
ER  -