scholarly journals Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth

2020 ◽  
Vol 293 (8) ◽  
pp. 1565-1590
Author(s):  
Antoine Pauthier ◽  
Arnd Scheel
Keyword(s):  
Crystal Growth ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Flux ◽  
Advection Diffusion ◽  
Diffusion Dynamics ◽  
Boundary Flux

scholarly journals CRITICAL CURVES FOR A COUPLED SYSTEM OF FAST DIFFUSIVE NEWTONIAN FILTRATION EQUATIONS

2012 ◽  
Vol 86 (3) ◽  
pp. 440-447
Author(s):  
RUNMEI DU ◽  
ZEJIA WANG
Keyword(s):  
Nonlinear Boundary ◽  
Large Time ◽  
Upper And Lower Solutions ◽  
Coupled System ◽  
Dimensional System ◽  
Nonlinear Boundary Flux ◽  
One Dimensional ◽  
Critical Curves ◽  
Nonlinear Anal ◽  
Boundary Flux

AbstractThis paper deals with the large-time behaviour of solutions to the fast diffusive Newtonian filtration equations coupled via the nonlinear boundary sources. A result of Fujita type is obtained by constructing various kinds of upper and lower solutions. In particular, it is shown that the critical global existence curve and the critical Fujita curve concide for the multi-dimensional system. This is quite different from the known results obtained in Wang, Zhou and Lou [‘Critical exponents for porous medium systems coupled via nonlinear boundary flux’, Nonlinear Anal.7(1) (2009), 2134–2140] for the corresponding one-dimensional problem.

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