scholarly journals Uniqueness of solutions to the initial-value problem for partial differential equations with multiple characteristics

1985 ◽  
Vol 11 (1-3) ◽  
pp. 293-305
Author(s):  
Marvin Zeman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Partial Differential ◽  
Multiple Characteristics

The initial-value problem for long waves of finite amplitude

1964 ◽  
Vol 20 (1) ◽  
pp. 161-170 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Integration ◽  
Initial Value Problem ◽  
Finite Amplitude ◽  
Long Waves ◽  
Initial Value ◽  
Partial Differential ◽  
Long Wave ◽  
Constant Slope

Derived herein is a set of partial differential equations governing the propagation of an arbitrary, long-wave disturbance of small, but finite amplitude. The equations reduce to that of Boussinesq (1872) when the assumption is made that the disturbance is propagating in one direction only. The equations are hyperbolic with characteristic curves of constant slope. The initial-value problem can be solved very readily by numerical integration along characteristics. A few examples are included.

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