General asymptotic supnorm estimates for solutions of one-dimensional advection-diffusion equations in heterogeneous media
type: Item
instance of: scholarly article
title: General asymptotic supnorm estimates for solutions of one-dimensional advection-diffusion equations in heterogeneous media
zbMATH Open document ID: 1304.35145
DOI: 10.1155/2014/450417
author: José A. Barrionuevo
author: Lucas S. Oliveira
author: Paulo R. Zingano
published in: International Journal of Partial Differential Equations
publication date: 2014-09-30T00:00:00Z
review text: Summary: We derive general bounds for the large time size of supnorm values \(\| u(\cdot,t)\|_{L^\infty(\mathbb R)}\) of solutions to one-dimensional advection-diffusion equations \(u_t+(b(x,t)u)_x=u_{xx}\), \(x\in\mathbb R\), \(t>0\) with initial data \(u(\cdot,0)\in L^{p_0}(\mathbb R)\cap L^\infty(\mathbb R)\) for some \(1\leq p_0<\infty\) and arbitrary bounded advection speeds \(b(x,t)\), introducing new techniques based on suitable energy arguments. Some open problems and related results are also given.
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 6349586
zbMATH Keywords: one space dimension
zbMATH Keywords: arbitrary bounded advection speeds
Wikidata QID: Q59051413
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/450417
OpenAlex ID: W2030225704
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description: scientific article; zbMATH DE number 6349586