A REMARK ON LARGE TIME ASYMTOTICS FOR SOLUTIONS OF A NONHOMOGENEOUS VISCOUS BURGERS EQUATION*

doi:10.1007/s10473-023-0318-x

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1323-1332.doi: 10.1007/s10473-023-0318-x

A REMARK ON LARGE TIME ASYMTOTICS FOR SOLUTIONS OF A NONHOMOGENEOUS VISCOUS BURGERS EQUATION^*

Manas Ranjan Sahoo¹, Satyanarayana Engu^2,†, Smriti Tiwari²

1. School of Mathematical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, P. O. Jatni, Khurda, Odisha 752050, India;
2. Department of Mathematics, National Institute of Technology Warangal 506004, Telangana, India

收稿日期:2021-05-12 修回日期:2021-12-13 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Satyanarayana Engu,E-mail: satya@nitw.ac.in
作者简介:Manas Ranjan Sahoo,E-mail: manas@niser.ac.in;Smriti Tiwari, E-mail: smriti19@student.nitw.ac.in
基金资助:
S. Engu was supported by Council of Scientific and Industrial Research, India (File no. 25 (0302)/19/EMR-II ).

A REMARK ON LARGE TIME ASYMTOTICS FOR SOLUTIONS OF A NONHOMOGENEOUS VISCOUS BURGERS EQUATION^*

Manas Ranjan Sahoo¹, Satyanarayana Engu^2,†, Smriti Tiwari²

1. School of Mathematical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, P. O. Jatni, Khurda, Odisha 752050, India;
2. Department of Mathematics, National Institute of Technology Warangal 506004, Telangana, India

Received:2021-05-12 Revised:2021-12-13 Online:2023-06-25 Published:2023-06-06
Contact: ^† Satyanarayana Engu,E-mail: satya@nitw.ac.in
About author:Manas Ranjan Sahoo,E-mail: manas@niser.ac.in;Smriti Tiwari, E-mail: smriti19@student.nitw.ac.in
Supported by:
S. Engu was supported by Council of Scientific and Industrial Research, India (File no. 25 (0302)/19/EMR-II ).

摘要/Abstract

摘要： The existence, uniqueness and regularity of solutions to the Cauchy problem posed for a nonhomogeneous viscous Burger's equation were shown in Chung, Kim and Slemrod [1] by assuming suitable conditions on initial data. Moreover, they derived the asymptotic behaviour of solutions of the Cauchy problem by imposing additional conditions on initial data. In this article, we obtain the same asymptotic behaviour of solutions to the Cauchy problem without imposing additional condition on initial data.

关键词: modified Bessel functions, integral equation, large time asymptotics, convolution of functions

Abstract: The existence, uniqueness and regularity of solutions to the Cauchy problem posed for a nonhomogeneous viscous Burger's equation were shown in Chung, Kim and Slemrod [1] by assuming suitable conditions on initial data. Moreover, they derived the asymptotic behaviour of solutions of the Cauchy problem by imposing additional conditions on initial data. In this article, we obtain the same asymptotic behaviour of solutions to the Cauchy problem without imposing additional condition on initial data.

Key words: modified Bessel functions, integral equation, large time asymptotics, convolution of functions

Manas Ranjan Sahoo, Satyanarayana Engu, Smriti Tiwari. A REMARK ON LARGE TIME ASYMTOTICS FOR SOLUTIONS OF A NONHOMOGENEOUS VISCOUS BURGERS EQUATION^*[J]. 数学物理学报(英文版), 2023, 43(3): 1323-1332.

Manas Ranjan Sahoo, Satyanarayana Engu, Smriti Tiwari. A REMARK ON LARGE TIME ASYMTOTICS FOR SOLUTIONS OF A NONHOMOGENEOUS VISCOUS BURGERS EQUATION^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1323-1332.

参考文献

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A REMARK ON LARGE TIME ASYMTOTICS FOR SOLUTIONS OF A NONHOMOGENEOUS VISCOUS BURGERS EQUATION^*

A REMARK ON LARGE TIME ASYMTOTICS FOR SOLUTIONS OF A NONHOMOGENEOUS VISCOUS BURGERS EQUATION^*

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