scholarly journals Singular limits of reaction diffusion equations and geometric flows with discontinuous velocity

2020 ◽  
Vol 200 ◽  
pp. 111989
Author(s):  
Cecilia De Zan ◽  
Pierpaolo Soravia
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Geometric Flows ◽  
Singular Limits

scholarly journals A PDE model for bleb formation and interaction with linker proteins

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Philipp Werner ◽  
Martin Burger ◽  
Jan-Frederik Pietschmann
Keyword(s):  
Fluid Dynamics ◽  
Cell Membrane ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Pde Model ◽  
Nonlinear Reaction ◽  
Singular Limits ◽  
Bleb Formation ◽  
Detailed Mathematical Analysis

Abstract The aim of this paper is to further develop mathematical models for bleb formation in cells, including cell membrane interactions with linker proteins. This leads to nonlinear reaction–diffusion equations on a surface coupled to fluid dynamics in the bulk. We provide a detailed mathematical analysis and investigate some singular limits of the model, connecting it to previous literature. Moreover, we provide numerical simulations in different scenarios, confirming that the model can reproduce experimental results on bleb initiation.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Sign in / Sign up

Export Citation Format

Share Document