On a quasi-linear parabolic equation occurring in aerodynamics

By J. Cole. 1951

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1. J. Gray
2. C. Ancey
3. Martin Hairer
4. Fabrice Baudoin
5. J. Bec
6. Bai-lian Li
7. Sergei V. Petrovskii
8. Joachim Krug

Citations in the corpus

• A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, methodology): “which was originally applied to the deterministic Burgers equation [30, 56] and rediscovered in the context of (33) by Huse, Henley and Fisher [57].”
• Existence and Smoothness of Navier-Stokes Equations (2018, background): “The equation is the simplest model equation that can describe the second order nonlinear effects connected with the propagation of high-amplitude (finiteamplitude waves) plane waves and, in addition, the dissipative effects in real fluids [9, 11, 12, 13, 14, 18].”
• Multi-component particle-size segregation in shallow granular avalanches (2011, methodology): “…is closely related to Burgers’ equation, which Gray & Chugunov (2006) exploited to construct exact solutions for time-dependent segregation, by using the Cole–Hopf transformation (Hopf 1950; Cole 1951) to linearize both the segregation–remixing equation (3.6) and the boundary conditions (2.32).”
• Generalized finite-difference schemes (1969, background): “) Cole [4] exhibits the exact solution of Burgers' equation with such discontinuous data for the pure initial-value problem; it is a wave traveling to the right at velocity 1/2 which has the shape (asymptotically, as t becomes large) of [1 — tanh (a:/4«)]/2.”
• On an accurate third order implicit-explicit Runge--Kutta method for stiff problems (2009, methodology): “The exact solution of this problem was obtained by Cole [8] so that numerical comparison can be done.”