Satyanarayana Engu, Manas R. Sahoo, Venkatramana P. Berke
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 infinity.
Submitted January 19, 2019. Published January 7, 2021.
Math Subject Classifications: 35C15, 35K05, 35K20, 35B09, 35B40.
Key Words: Abel integral equation; Hopf transformation; heat equation;
large time asymptotic; weak solutions.
DOI: https://doi.org/10.58997/ejde.2021.02
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Satyanarayana Engu Department of Mathematics National Institute of Technology, Warangal Telangana-506004, India email: satya@nitw.ac.in |
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Manas R. Sahoo School of Mathematical Sciences National Institute of Science Education and Research HBNI, Jatni, Khurda, Bhubaneswar 752050, India email: manas@niser.ac.in |
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Venkatramana P. Berke Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, Surathkal Shrinivas Nagar, Mangalore-575025, India email: venkat.nitk19@gmail.com |
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