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The contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock
Geng Chen, Harish Ravichandar, Yannan Shen
The paper proves that planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev‑Petviashvili equation and the multi‑dimensional KdV‑Burgers equation con…
-contraction of Shock Waves for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave sol…
Uniform Stability of Oscillatory Shocks for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
We study viscous-dispersive shock waves with infinite oscillations of the Korteweg-de Vries-Burgers (KdVB) equation. First, we establish detail structures of the shock waves, inclu…
Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry
Geng Chen, Faris A. El-Katri, Yanbo Hu +1
In this paper, we consider the singularity formation of smooth solutions for the compressible radially symmetric Euler equations. By applying the characteristic method and the inva…
Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
Geng Chen, Faris A. El-Katri, Yanbo Hu +1
In this paper, we define the rarefaction and compression characters for the supersonic expanding wave of the compressible Euler equations with radial symmetry. Under this new defin…