Smooth solutions of u_tt - u_xx = (u_x)^2 admit stable, explicitly written blow-up profiles with logarithmic growth, and no smooth exact self-similar blow-up exists.
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Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity
Smooth solutions of u_tt - u_xx = (u_x)^2 admit stable, explicitly written blow-up profiles with logarithmic growth, and no smooth exact self-similar blow-up exists.