A formal solution of the equation for mean flow of energy due to momentum fluctuations is presented, leading to a definition of local fluctuating dynamical equilibrium of a time-stationary flow and an identification of sources of far field radiated acoustic power.
Also, application of this operator for obtaining a formal solution of the time-fractional telegraph equation is discussed.
These calculations use numerical methods based on a formal solution of the time-dependent radiation transfer equation, eliminating the need for approximate closures.
A formal solution is obtained for the scattered pressure, and investigated asymptotically for the case of heavy exterior fluid loading.
A formal solution is obtained for the scattered pressure and investigated asymptotically for the case of smallkaand heavy interior fluid loading.
In Section 4.1, we introduce an auxiliary differential and convolution problem (70) for which we construct a formal solution.
In spite of that, Peano elaborated a formal solution.
However, it is lacking a formal solution to resolving ambiguous matches.
The approach is based upon inversion of the formal solution for the direct problem and assumes that data are available on a regular grid at successive time steps.
