Solutions to viscous Burgers equations with time dependent source term

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 bo...

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Bibliographic Details
Published in:Electronic journal of differential equations 2021-01, Vol.2021 (1-104), p.2
Main Authors: Engu, Satyanarayana, Sahoo, Manas R., Berke, Venkatramana P.
Format: Article
Language:English
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Summary: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 infinity. For more information see https://ejde.math.txstate.edu/Volumes/2021/02/abstr.html
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2021.02