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Black dots indicate a minimum wave speed c0 for each value of W0.
Under the so-called quasi-monotonicity assumption, we use the upper-lower solution method and Schauder's fixed point theorem to establish the existence of traveling wave and obtain an explicit expression of the minimum wave speed (c^).
Assuming that the full nonlinear system supports a pulled front, then a sufficiently localized initial perturbation (one that decays faster than e - λ 0 x ) will asymptotically approach the traveling front solution with the minimum wave speed c0 = c λ0).
Furthermore, the minimum wave speed (required for the closure of cavitation modelling in the sonochemical reactor design) is analyzed and the influences of paramount parameters on it are quantitatively discussed.
Linearising ahead of the wave, the p-equation decouples and a travelling wave analysis indicates that there is a minimum wave speed which is independent of δ.
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By modifying the maximum-minimum wave speed, the problem of expansion shock and numerical instability in the expansion region is also remedied without sacrificing the exact capturing of contact discontinuity.
In the FDM simulation, the model has a minimum P wave speed (Vp = 1.5 km/s) in seawater and a minimum S wave speed (Vs = 3.5 km/s) in the upper crust, which allows for S wave propagation simulations at frequencies less than 1.5 Hz, with a sampling rate of 3.5 grid points per minimum S wavelength.
It is assumed that the load has a constant magnitude, moves along a straight line normal to the interface, and has a constant speed that is smaller than the minimum shear wave speed in the half-planes.
The maximum wave speed is known as soon as the media are specified, while the minimum spatial stepsizes are known after the configuration has been discretized.
The deep minimum in the wave speed in the ionosphere forms a resonant cavity, termed the ionospheric Alfvén resonator (IAR) by Polyakov and Rapoport (1981) and studied extensively by (Trakhtengertz and Feldstein 1984 , 1991 and (Lysak 1986 , 1991 , 1993
Wave speed asymptotically approaches the minimum c0 of the velocity dispersion curve given by Equation 2.12. Figure 6 Propagating front in a network with a linear heterogeneity ( ε 2 = 0.005).
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