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Zbl 1124.35318
Petitta, Francesco
Asymptotic behavior of solutions for linear parabolic equations with general measure data.
(English)
[J] C. R., Math., Acad. Sci. Paris 344, No. 9, 571-576 (2007). ISSN 1631-073X

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 2000:
*35K15 Second order parabolic equations, initial value problems
35R05 PDE with discontinuous coefficients or data
35B40 Asymptotic behavior of solutions of PDE

Citations: Zbl 0151.15401

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