Browsing by Author "Satyanarayana, E."

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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.
Large Time Asymptotics with Error Estimates to Solutions of a Forced Burgers Equation
(2017) Satyanarayana, E.; Ahmed, M.; Murugan, V.
This article deals with a forced Burgers equation (FBE) subject to the initial function, which is continuous and summable on R. Large time asymptotic behavior of solutions to the FBE is determined with precise error estimates. To achieve this, we construct solutions for the FBE with a different initial class of functions using the method of separation of variables and Cole Hopf like transformation. These solutions are constructed in terms of Hermite polynomials with the help of similarity variables. The constructed solutions would help us to pick up an asymptotic approximation and to show that the magnitude of the difference function of the true and approximate solutions decays algebraically to 0 for large time. 2016 Wiley Periodicals, Inc., A Wiley Company
Large Time Asymptotics with Error Estimates to Solutions of a Forced Burgers Equation
(2017) Satyanarayana, E.; Mohd, M.; Murugan, V.
This article deals with a forced Burgers equation (FBE) subject to the initial function, which is continuous and summable on R. Large time asymptotic behavior of solutions to the FBE is determined with precise error estimates. To achieve this, we construct solutions for the FBE with a different initial class of functions using the method of separation of variables and Cole–Hopf like transformation. These solutions are constructed in terms of Hermite polynomials with the help of similarity variables. The constructed solutions would help us to pick up an asymptotic approximation and to show that the magnitude of the difference function of the true and approximate solutions decays algebraically to 0 for large time. © 2016 Wiley Periodicals, Inc., A Wiley Company
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.