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math-ph2025
Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity
Amit Acharya
The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This…
math.AP2025
On the variational dual formulation of the Nash system and an adaptive convex gradient-flow approach to nonlinear PDEs
Dmitry Vorotnikov, Amit Acharya
We investigate the influence of base states on the consistency of the dual variational formulation for quadratic systems of PDEs, which are not necessarily conservative (typical ex…
math.OC2025
A convex variational principle for the necessary conditions of classical optimal control
Amit Acharya, Janusz Ginster
A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary c…