Finite speed of propagation and asymptotic rates for some nonlinear higher order parabolic equations with absorption
Francisco Bernis · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1986
Synopsis The “energy solutions” to the equation have finite speed of propagation if l 0 (localisation property) and if q<2 ≦ r , sharp upper bounds of the interface (or free boundary) are obtained. We use a weighted energy method, the weights being powers of the distance to a variable half-space. We also study decay rates as t→∞ and extinction in finite time for bounded and unbounded domains (with null Dirichlet boundary conditions). Our equation includes the porous media equation with absorption. Analogous results hold if (−Δ) m is replaced by an appropriate quasilinear elliptic operator.