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January  2017, 16(1): 253-272. doi: 10.3934/cpaa.2017012

## Higher order asymptotic for Burgers equation and Adhesion model

 1 Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Mangalore-575 025, India 2 School of Mathematical Sciences, National Institute of Science Education and Research, Bhimpur-Padanpur, Via-Jatni, Khurda-752050, Odisha, India 3 Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Mangalore-575 025, India

Manas R. Sahoo, E-mail address: manas@niser.ac.in

Received  April 2016 Revised  September 2016 Published  November 2016

This paper is focused on the study of the large time asymptotic for solutions to the viscous Burgers equation and also to the adhesion model via heat equation. Using generalization of the truncated moment problem to a complex measure space, we construct asymptotic N-wave approximate solution to the heat equation subject to the initial data whose moments exist upto the order $2n+m$ and $i$-th order moment vanishes, for $i=0, 1, 2\dots m-1$. We provide a different proof for a theorem given by Duoandikoetxea and Zuazua [3], which plays a crucial role in error estimations. In addition to this we describe a simple way to construct an initial data in Schwartz class whose $m$ moments are equal to the $m$ moments of given initial data.

Citation: Engu Satynarayana, Manas R. Sahoo, Manasa M. Higher order asymptotic for Burgers equation and Adhesion model. Communications on Pure & Applied Analysis, 2017, 16 (1) : 253-272. doi: 10.3934/cpaa.2017012
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