OurBigBook.comSite Source code

Energy dissipation identity for a linearly damped string

For fixed endpoints and

E (t) = \frac{1}{2} \int_{0}^{1} (y_{t}^{2} + y_{x}^{2}) d x,

integration by parts and the damped wave equation give

E^{'} (t) = - \int_{0}^{1} y_{t}^{2} d x \leq 0.

 Ancestors (8)

 Incoming links (1)

Solution