Cauchy vs. Dirichelt/Neumann Condition for PDE

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SUMMARY

The discussion clarifies the distinctions between Cauchy boundary conditions and combined Dirichlet/Neumann boundary conditions for partial differential equations (PDEs). Cauchy conditions, which specify both the function u and its normal derivative du/dn on a boundary C, are applicable for solving Open Hyperbolic PDEs. In contrast, Dirichlet conditions provide the function u on the boundary, while Neumann conditions specify the normal derivative du/dn. The combination of Dirichlet and Neumann conditions does not constitute a Cauchy condition.

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  • Understanding of partial differential equations (PDEs)
  • Familiarity with boundary conditions in mathematical analysis
  • Knowledge of Open Hyperbolic, Elliptic, and Parabolic PDEs
  • Basic concepts of function derivatives and normal derivatives
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ginarific
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Hi,

Can anybody tell me the difference between a Cauchy Boundary condition and a combined Dirichlet/Neumann Boundary Condition for PDEs?

The reason why I'm asking is because Cauchy boundary conditions can be used to solve Open Hyperbolic PDEs, whereas Dirichlet/Neumann can only be used to solve Elliptic and Parabolic PDEs.

My textbook says:

Cauchy Conditions: have u and du/dn given on C

Dirichlet Conditions: have u given on C

Neumann Conditions: du/dn given on C

So if you have a combination of Dirichlet and Neumann conditions, is that a Cauchy condition?

Any help would be much appreciated!

Thanks,
Gina
 
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If it helps at all, I think I've seen some discussion on these BC's inhttp://youtu.be/-BleG7PBwEA" .
 
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