
doi: 10.5802/jedp.442
The Cauchy problem for the dissipative wave equation \[ u_{tt} - \Delta u + u | u |^ p = 0, \quad t > 0, \quad x \in \mathbb{R}^ d \] with fast oscillating initial functions is considered. The problem is a passage of the fast oscillating wave through a focal point, where the wave amplitude is increasing that is predicted by the geometric optics method. The main result is as follows: The oscillations which may be present in the initial data do not survive a passage through the focus, if \((d-1)p \geq 2\).
fast oscillating initial functions, Geometric optics, Second-order nonlinear hyperbolic equations, passage of the fast oscillating wave through a focal point
fast oscillating initial functions, Geometric optics, Second-order nonlinear hyperbolic equations, passage of the fast oscillating wave through a focal point
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 2 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
