Scaling Variables and Asymptotic Expansions in Damped Wave Equations

Expansions and eigenfrequencies for damped wave equations

We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that the...

Eigenfrequencies and expansions for damped wave equations

We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. Under the assumption of geometric control, the propagator is shown to admit an expansion in terms of finitely many eigenmodes near the real axis, with an error term exponentially decaying in time. In the presence of a nondegenerate elliptic closed geodesic not meeting the support of the damping c...

Asymptotic Expansion for Damped Wave Equations with Periodic Coefficients

Composite asymptotic expansions and scaling wall turbulence.

In this article, the assumptions and reasoning that yield composite asymptotic expansions for wall turbulence are discussed. Particular attention is paid to the scaling quantities that are used to render the variables non-dimensional and of order one. An asymptotic expansion is proposed for the streamwise Reynolds stress that accounts for the active and inactive turbulence by using different sc...

Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation

We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted L and L∞ estimates. Furthermore, we establish the higher order asymptotic expansion of the solution. This means that we construct the nonlinear approximation of the global solution with respect to the weigh...