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Blow-up rates and sets for a quasilinear diffusion equation with weighted source

math.AP · 2026-04-06 · unverdicted · novelty 5.0

For the equation ∂t u = Δu^m + |x|^σ u^p with 1 < p < m and σ > 0, compactly supported solutions satisfy C1 (T-t)^{-α} ≤ ||u(·,t)||_∞ ≤ C2 (T-t)^{-α} and support radius ≤ C0 (T-t)^{-β} with α = (σ+2)/L, β = (m-p)/L, L = σ(m-1) + 2(p-1), and blow-up sets are either all of R^N or only at infinity.

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  • Blow-up rates and sets for a quasilinear diffusion equation with weighted source math.AP · 2026-04-06 · unverdicted · none · ref 8

    For the equation ∂t u = Δu^m + |x|^σ u^p with 1 < p < m and σ > 0, compactly supported solutions satisfy C1 (T-t)^{-α} ≤ ||u(·,t)||_∞ ≤ C2 (T-t)^{-α} and support radius ≤ C0 (T-t)^{-β} with α = (σ+2)/L, β = (m-p)/L, L = σ(m-1) + 2(p-1), and blow-up sets are either all of R^N or only at infinity.