Browsing by Author "Sahoo, M.R."

Now showing 1 - 7 of 7

Asymptotic Behavior of Solutions to the Diffusion Equation
(2018) Engu, 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.
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.
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.
On a complex sequence of vanishing moments
(2019) Sahoo, M.R.; Satyanarayana, E.; Sen, A.
This paper shows that vanishing of all moments of the complex sequence {zj} implies that {zj} is identically zero, provided {zj} is in lp,1 ? p < ?. This proof is different from one given by Priestley [Proc. Amer. Math. Soc. 116 (1992) 437 444] and shows an interesting connection of this problem with heat kernel. 2019 Ramanujan Mathematical Society. All rights reserved.
On a complex sequence of vanishing moments
(Ramanujan Mathematical Society, 2019) Sahoo, M.R.; Satyanarayana, E.; Sen, A.
This paper shows that vanishing of all moments of the complex sequence {zj} implies that {zj} is identically zero, provided {zj} is in lp,1 ? p < ?. This proof is different from one given by Priestley [Proc. Amer. Math. Soc. 116 (1992) 437–444] and shows an interesting connection of this problem with heat kernel. © 2019 Ramanujan Mathematical Society. All rights reserved.
Solutions to viscous burgers equations with time dependent source term
(Texas State University - San Marcos, 2021) Satyanarayana, S.; Sahoo, M.R.; Berke, V.P.
We study the existence and uniqueness of weak solutions for a Cauchy problem of a viscous Burgers equation with a time dependent reaction term involving Dirac measure. After applying a Hopf like transformation, we investigate the associated two initial boundary value problems by assuming a common boundary. The existence of the boundary data is shown with the help of Abel’s integral equation. We then derive explicit representation of the boundary function. Also, we prove that the solutions of associated initial boundary value problems converge uniformly to a nonzero constant on compact sets as t approaches ?. © 2021 Texas State University.