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element of [0, infinity) with tau >= 0, m > 1 and suitable density functions f (y). We apply this correspondence to the case of constant coefficients a(x) =1 and b(x) = K > 0. For this case, we prove that compactly supported solutions to the first equation blow up in finite time, together with their interfaces, as x -> -infinity. We then establish the large time behavior of solutions to a homogeneous Dirichlet problem associated to the first equation on a bounded interval. We also prove a finite time blow-up of the interfaces for compactly supported solutions to the second equation when f(y) = y(-gamma) with gamma > 2. (C) 2019 Elsevier Inc. 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