Eternal solutions to a porous medium equation with strong nonhomogeneous absorption. Part II: Dead-core profiles

Existence of a specific family of eternal solutions in exponential self-similar form is proved for the following porous medium equation with strong absorption: [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. Looking for solutions of the form [Formula: see text] it is shown that, for [Formula: see text], there exists a unique exponent [Formula: see text] for which there exists a one-parameter family of compactly supported profiles presenting a dead core. The precise behavior of the profiles at their interface is also determined. Moreover, the corresponding solutions show the optimal limitations for the finite time extinction property of genuine non-negative solutions to the Cauchy problem, studied in previous works.