Solutions to viscous Burgers equations with time dependent source term
| dc.contributor.author | Engu, Satyanarayana | |
| dc.contributor.author | Sahoo, Manas | |
| dc.contributor.author | Berke, Venkatramana | |
| dc.date.accessioned | 2021-08-19T19:07:11Z | |
| dc.date.available | 2021-08-19T19:07:11Z | |
| dc.date.issued | 2021-01-07 | |
| dc.description.abstract | 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 ∞. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Engu, S., Sahoo, M. R., & Berke, V. P. (2021). Solutions to viscous Burgers equations with time dependent source term. <i>Electronic Journal of Differential Equations, 2021</i>(02), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14399 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Abel integral equation | |
| dc.subject | Hopf transformation | |
| dc.subject | Heat equation | |
| dc.subject | Large time asymptotic | |
| dc.subject | Weak solutions | |
| dc.title | Solutions to viscous Burgers equations with time dependent source term | |
| dc.type | Article |