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Asymptotic behavior of solutions for linear parabolic equations with general measure data. (English) Zbl 1124.35318

Summary: In this note we deal with the asymptotic behavior as t tends to infinity of solutions for linear parabolic equations whose model is

u t -Δu=μin(0,T)×Ω,u(0,x)=u 0 inΩ,

where μ is a general, possibly singular, Radon measure which does not depend on time, and u 0 L 1 (Ω). We prove that the duality solution, which exists and is unique, converges to the duality solution (as introduced by G. Stampacchia [Ann. Inst. Fourier 15, No. 1, 189–257 (1965) and Colloques Int. Centre nat. Rech. Sci. 146, 189–258 (1965; Zbl 0151.15401)]) of the associated elliptic problem.

35K15Second order parabolic equations, initial value problems
35R05PDEs with discontinuous coefficients or data
35B40Asymptotic behavior of solutions of PDE
Radon measure