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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 $$\cases u_t-\Delta u=\mu &\text{in }(0,T)\times\Omega,\\ u(0,x)= u_0 &\text{in }\Omega,\endcases$$ where $\mu$ is a general, possibly singular, Radon measure which does not depend on time, and $u_0\in L^1(\Omega)$. We prove that the duality solution, which exists and is unique, converges to the duality solution (as introduced by {\it 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.

##### MSC:
 35K15 Second order parabolic equations, initial value problems 35R05 PDEs with discontinuous coefficients or data 35B40 Asymptotic behavior of solutions of PDE
##### Keywords:
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