Convergence to Strong Nonlinear Diffusion Waves for Solutions of p-System with Damping

Initial boundary value problem for compressible Euler equations with damping

“…In this direction, the readers are referred to [31], [13], [14] and [12] for existence of small smooth solutions; to [27], [4], and [6] for solutions in BV ; to [7] and [20] for L ∞ solutions. For large time behavior of solutions, we refer [13], [14], [33], [34] and [45] fore small smooth solutions; and we refer [19], [21], [39] and [47] for weak solutions. For initial boundary value problems, see [16], [28] and [35] for small smooth solutions.…”

Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

“…In these procedure, we have overcome the difficulty from the coupling and cancelation interaction between n 1 and n 2 . Finally, it is worth mentioning that similar results about the Euler equations with damping have been extensively studied by many authors, i.e., the authors of [16][17][18][19]21,22], etc.…”

The strong relaxation limit of the multidimensional Euler equations

“…After that, such problem was widely studied by many authors, see e.g., among many other works [6,7,11,15,20,22] and references therein for further results. A closely related-though not exactly equivalent-problem is to study the behavior of the solutions to the strong relaxation model as the relaxation time ε in (1) tends to 0.…”