Solutions to viscous Burgers equations with time dependent source term




Engu, Satyanarayana
Sahoo, Manas
Berke, Venkatramana

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Texas State University, Department of Mathematics


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 ∞.



Abel integral equation, Hopf transformation, Heat equation, Large time asymptotic, Weak solutions


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.


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