What Equation Combines Laplacian and Time Derivatives of a Vector Function?

[Schreiberdk]

Hi PF

I need help with identifying an equation. It contains the following:

The sum of: The laplacian of a vectorfunction, the second time derivative of a vectorfunction and the first time derivative of a vectorfunction, which is all equal to zero.

Laplacian(V)+d^2/dt^2(V)+d/dt(V)=0

Anyone got any suggestions, of which equation this might look like, or any specific physical uses of the equation?

 

[AiRAVATA]

It is the Newton equation for the small displacement of a string (or membrane, etc.) considering friction.

 

[Schreiberdk]

So it is a wave equation taking friction into account?

 

[AiRAVATA]

Indeed.---EDIT---

Err, not quite. I hadn't noticed the sign of the Laplacian.

 

[blue_raver22]

Sure, I can help you with this equation. It appears to be describing the behavior of a vector function in terms of its second and first time derivatives, as well as its Laplacian. This type of equation is commonly seen in physics and engineering, particularly in the study of wave propagation and oscillations. It could also be used to describe the motion of a particle in a conservative force field. Without more context, it is difficult to pinpoint a specific physical application, but I hope this information helps you in your understanding of the equation.