For a new 1D boundary-layer model of the porous media equation with nonlocal velocity, smooth even data that vanish at the origin and increase toward the edge lose smoothness in finite time.
Dong, Well-posedness for a transport equation with non-local vel ocity, J
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Finite time blow-up in a 1D model of the incompressible porous media equation
For a new 1D boundary-layer model of the porous media equation with nonlocal velocity, smooth even data that vanish at the origin and increase toward the edge lose smoothness in finite time.