scholarly journals Group classification of variable coefficient quasilinear reaction-diffusion equations

2013 ◽  
Vol 94 (108) ◽  
pp. 81-90 ◽  
Author(s):  
Olena Vaneeva ◽  
Alexander Zhalij
Keyword(s):  
Variable Coefficient ◽  
Reaction Diffusion ◽  
Group Classification ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Equivalence Group ◽  
Point Transformations

The group classification of variable coefficient quasilinear reaction diffusion equations ut = uxx + h(x)B(u) is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the study of admissible point transformations within the class.

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.

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