Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Keywords: Radon measure

Citations: Zbl 0151.15401

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]