Convergence of the Dirichlet solutions of the very fast diffusion equation

2010/12/15 by Hui, Kin Ming, Kim, Sunghoon · 1 citation
#35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35B40 Secondary 35K15

paper · doi:10.48550/arxiv.1012.3218

Abstract

For any -10, 0≤ u₀∈ L^∞(R) such that u₀(x)≤ (μ₀ |m||x|)^(1)/(m) for any |x|≥ R₀ and some constants R₀>1 and 00, u(x,0)=u₀(x) in (-R,R), converges uniformly on every compact subsets of R× (0,T) to the solution of the equation u_t=(u^m/m)_xx in R× (0,∞), u(x,0)=u₀(x) in R, which satisfies ∫_Ru(x,t) dx=∫_Ru₀dx-∫₀^t(f(s)+g(s)) ds for all 0

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