The partial differential equation ut + uux = μxx

By E. Hopf. 1950

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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).”
On Lp-solutions of semilinear stochastic partial differential equations (2000, background): “A famous example in one space dimension is Burgers’ equation, when aij =1, =0, f=0; g(t; x; r)= 12 r 2 (see e.g. Burgers, 1948; Hopf, 1950; Liu and Yu, 1997), and the references therein).”