A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor

DOI10.3934/dcdsb.2016045zbMath1347.60086OpenAlexW2510239077MaRDI QIDQ316936

Christina Surulescu, Peter E. Kloeden, Stefanie Sonner

Publication date: 30 September 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2016045

zbMATH Keywords

stochastic differential equationsreaction-diffusion equationmean-field modelmultiscale modelnonlocal sample dependenceproton dynamicstumor acidity

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Reaction-diffusion equations (35K57) Medical applications (general) (92C50) Applications of stochastic analysis (to PDEs, etc.) (60H30) Ordinary differential equations and systems with randomness (34F05) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items

On a coupled SDE-PDE system modeling acid-mediated tumor invasion, Modeling of pH regulation in tumor cells: direct interaction between proton-coupled lactate transporters and cancer-associated carbonic anhydrase, A coupled stochastic differential reaction-diffusion system for angiogenesis, Viability in a non-local population model structured by size and spatial position, Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment, Mathematical Analysis and Numerical Simulations for the Cancer Tissue Invasion Model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic models in biology and the invariance problem
• A stochastic multiscale model for acid mediated cancer invasion
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Tumour-stromal interactions in acid-mediated invasion: a mathematical model
• The role of acidity in solid tumour growth and invasion
• A stochastic model featuring acid-induced gaps during tumor progression
• Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations
• Stochastic Differential Equations with Nonlocal Sample Dependence
• A multiscale model for pH-tactic invasion with time-varying carrying capacities
• Stochastic viability and a comparison theorem
• Noise-Induced Behaviors in Neural Mean Field Dynamics