Sharp existence results for self-similar solutions of semilinear wave equations

2000 ◽  
Vol 7 (3) ◽  
pp. 323-341 ◽  
Author(s):  
Hartmut Pecher
Keyword(s):  
Wave Equations ◽  
Existence Results ◽  
Semilinear Wave Equations ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Self-similar solutions of semilinear wave equations with a focusing nonlinearity

Nonlinearity ◽  
2007 ◽  
Vol 20 (9) ◽  
pp. 2061-2074 ◽  
Author(s):  
Piotr Bizoń ◽  
Dieter Maison ◽  
Arthur Wasserman
Keyword(s):  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Self Similar ◽  
Similar Solutions

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

2021 ◽  
pp. 43-54
Author(s):  
A. N. Krutov ◽  
◽  
S. Ya. Shkol’nikov ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Method ◽  
Wave Equations ◽  
Simple Wave ◽  
Kinematic Wave ◽  
Calculation Results ◽  
Self Similar ◽  
Similar Solutions ◽  
The Mathematical Model ◽  
Good Agreement

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

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