Faculty Publications

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    Higher order asymptotic for Burgers equation and adhesion model
    (American Institute of Mathematical Sciences PO Box 2604 Springfield MO 65801-2604, 2017) Satyanarayana, E.; Sahoo, M.R.; Manasa, M.
    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 . . . 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. © 2017, American Institute of Mathematical Sciences. All rights reserved.
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    Asymptotic Behavior of Solutions to the Diffusion Equation
    (Indian National Science Academy, 2018) Satyanarayana, S.; Mohd, A.; Sahoo, M.R.
    We study asymptotic behavior of solutions to an initial value problem posed for heat equation. For which, we construct an approximate solution to the initial value problem in terms of derivatives of Gaussian by incorporating the moments of initial function. Spatial shifts are introduced into the leading order term as well as penultimate term of the approximation. This paper is continuation to the work of Yanagisawa [14]. © 2018, The Indian National Science Academy.