Abstract.
Geometric properties of shape functions of self-similar solution to the equation \( u_t = u_{xx} + \lambda\vert u_x\vert^q \) are studied, \( \lambda \) and q are positive numbers. These shapes-the solutions of the corresponding nonlinear ODE-are of very different nature. The properties usually depend on three critical values of q (1, 3/2 and 2). For the range 1<q<2 the dependence of \( \lambda \) is more remarkable, for example there is no global existence in general.
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GUEDDA, M., KERSNER, R. Self-similar solutions to the generalized deterministic KPZ equation. Nodea, Nonlinear differ. equ. appl. 10, 1–13 (2003). https://doi.org/10.1007/s00030-003-1036-z
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DOI: https://doi.org/10.1007/s00030-003-1036-z