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- W2974423399 abstract "In this work, we construct a transformation between the solutions to the following reaction-convection-diffusion equation∂tu=(um)xx+a(x)(um)x+b(x)um, posed for x∈R, t≥0 and m>1, where a, b are two continuous real functions, and the solutions to the nonhomogeneous diffusion equation of porous medium typef(y)∂τθ=(θm)yy, posed in the half-line y∈[0,∞) with τ≥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→−∞. 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−γ with γ>2." @default.
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- W2974423399 date "2020-02-01" @default.
- W2974423399 modified "2023-10-18" @default.
- W2974423399 title "Equivalence and finite time blow-up of solutions and interfaces for two nonlinear diffusion equations" @default.
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- W2974423399 doi "https://doi.org/10.1016/j.jmaa.2019.123503" @default.
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