The Thin Viscous Flow Equation in Higher Space Dimensions
نویسندگان
چکیده
We prove local integral (entropy) estimates for nonnegative solutions of the fourth order degenerate parabolic equation u t + div(u n ru) = 0 in space dimensions two and three. These estimates enable us to show that solutions have nite speed of propagation if n 2 (1 8 ; 2) and that the support cannot shrink if the growth exponent n is larger than 3=2. In addition, we prove decay estimates for solutions of the Cauchy problem and a growth estimate for their support.
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