Browsing by Author "Manasa, M."

Now showing 1 - 3 of 3

Generalized solutions of an inhomogeneous inviscid Burgers equation
(Indian National Science Academy, 2022) Satyanarayana, S.; Manasa, M.; Berke, P.B.
We derive generalized solutions of an inhomogeneous inviscid Burgers equation using vanishing viscosity method. This is achieved with the classical solution of a concerned viscous inhomogeneous Burgers equation. We then study Riemann problem for a de-coupled system. The weak solutions of the system are explicitly obtained by Volpert product concept. There are infinitely many real valued solutions for the system in the case of rarefaction wave and the weak solutions consist of δ- measures in the case of shock wave. Motivated by the structure of weak solutions, we construct the explicit generalized solutions for a more general de-coupled system. © 2021, The Indian National Science Academy.
Higher order asymptotic for Burgers equation and adhesion model
(2017) Satynarayana, 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.
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.