Kirane, Mokhtar; Qafsaoui, Mahmoud On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form. (English) Zbl 1031.35052 Rev. Mat. Complut. 15, No. 2, 585-598 (2002). Summary: We consider the linear convection-diffusion equation associated to higher-order elliptic operators \[ \begin{gathered} u_t+{\mathcal L}_tu= a\nabla u\quad\text{on }\mathbb{R}^n\times (0,\infty),\\ u(0)= u_0\in L^1(\mathbb{R}^n),\end{gathered}\tag{1} \] where \(a\) is a constant vector in \(\mathbb{R}^n\), \(m\in\mathbb{N}^*\), \(n\geq 1\) and \({\mathcal L}_0\) belongs to a class of higher-order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on \(\mathbb{R}^n\). The aim of this paper is to study the asymptotic behavior, in \(L^p\) \((1\leq p\leq\infty)\), of the derivatives \(D^\gamma u(t)\) of the solution of (1) when \(t\) tends to \(\infty\). Cited in 3 Documents MSC: 35K30 Initial value problems for higher-order parabolic equations 35K25 Higher-order parabolic equations 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs 35A08 Fundamental solutions to PDEs Keywords:non-smooth bounded measurable coefficients PDFBibTeX XMLCite \textit{M. Kirane} and \textit{M. Qafsaoui}, Rev. Mat. Complut. 15, No. 2, 585--598 (2002; Zbl 1031.35052) Full Text: DOI EuDML