Degenerate parabolic equation with critical exponent derived from the kinetic theory: I: Generation of the weak solution (Q1028493)

The blowup mechanism of the solution to a degenerate parabolic equation with the space dimension greater than 2 is under consideration. The main result of this paper is the theorem about essence a weak solution of the equation \[ u_t = \frac{m-1}{m}\Delta u^m - \nabla\cdot (u\nabla\Gamma * u ), \quad u\geq 0\quad\text{in }\mathbb R^n\times (0, T). \]