2 papers
math.AP2025
Existence and uniqueness of solutions to Liouville equation
Alireza Ataei
We prove some general results on the existence and uniqueness of solutions to the Liouville equation. Then, we discuss the sharpness and possible generalizations. Finally, we give…
math.AP2023
Existence and uniqueness of the solutions to convection-diffusion equations
Alireza Ataei
In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove…