2022 年 74 巻 2 号 p. 591-627
Let (𝑢, 𝑣) be a nonnegative solution to the semilinear parabolic system
(P)\begin{cases}𝜕𝑡 𝑢 = 𝐷1 Δ 𝑢 + 𝑣𝑝,𝑥 ∈ 𝐑𝑁, 𝑡 > 0,𝜕𝑡 𝑣= 𝐷2 Δ 𝑣 + 𝑢𝑞,𝑥 ∈ 𝐑𝑁, 𝑡 > 0,(𝑢(⋅,0), 𝑣(⋅,0))= (𝜇, 𝜈), 𝑥 ∈ 𝐑𝑁,\end{cases}
where 𝐷1, 𝐷2 > 0, 0 < 𝑝 ≤ 𝑞 with 𝑝𝑞 > 1 and (𝜇, 𝜈) is a pair of nonnegative Radon measures or nonnegative measurable functions in 𝐑𝑁. In this paper we study sufficient conditions on the initial data for the solvability of problem (P) and clarify optimal singularities of the initial functions for the solvability.
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