Global solution for a coupled parabolic system with degenerate coefficients and time-weighted sources

2022/09/11 by Castillo, Ricardo, Guzmán-Rea, Omar, Loayza, Miguel +1
#35A01 #35B33 #35K05 #35K58 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.04781

Abstract

In this paper, we obtain the so-called Fujita exponent to the following parabolic system with time-weighted sources and degenerate coefficients u_t- div ( ω(x)∇ u )= t^r v^p and v_t- div ( ω(x)∇ v )= t^s u^p in ℝ^N × (0,T) with initial data belonging to [L^∞(ℝ^N)]². Where p,q > 0 with pq > 1; r,s>-1 ; and either ω(x) = | x₁|^a, or ω(x) = | x |^b with a,b > 0.

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