scholarly journals Eigenvalues of Elliptic Systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions

2020 ◽  
Vol 33 (1) ◽  
pp. 48-63
Author(s):  
global sci
Keyword(s):  
Boundary Conditions ◽  
Mixed Problem ◽  
Neumann Boundary ◽  
Elliptic Systems ◽  
Neumann Boundary Conditions ◽  
Lipschitz Domains

scholarly journals Exact solution of problems of diffraction of unsteady waves on a wedge under mixed boundary conditions by the Smirnov-Sobolev method

2019 ◽  
Vol 485 (4) ◽  
pp. 434-437
Author(s):  
M. Sh. Israilov
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Mixed Boundary Conditions ◽  
Blast Waves ◽  
Neumann Boundary Conditions

Antil now, the Smirnov-Sobolev method has been applied only to diffraction problems with the Dirichlet and Neumann boundary conditions. In this study, it is shown that the method also leads to an exact solution of the mixed problem of diffraction on a wedge, which is very important, for example, for estimating the possibility of protection from blast waves by wedge-shaped barriers with different reflecting properties of the sides.

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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