2 citations · 2 across the 11 of their papers we have counts for
13 papers
Solving the Dissipation Inequality not as a constitutive restriction
Maximiliano Larrain Silva, Amit Acharya
A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality as a constraint equation within continuum mechanics, and allowing for incomplete kno…
Dual Variational Principles for Curl Forces
Arash Yavari, Amit Acharya
Curl forces are position-dependent, non-conservative, and non-dissipative forces that, in general, cannot be derived from an ordinary potential energy. Consequently, their equation…
Estimates on elliptic equations that hold only where the Hessian is large
Amit Kumar Acharya, Ram Baran Verma
In this article, we establish Hölder regularity for viscosity solutions to a class of degenerate fully nonlinear elliptic equations of the form \[ F(D^2u,Du)=f(x)~~\text{in}~~B_1,…
Liouville type theorems for fully nonlinear elliptic equations with superlinear growth in gradient
Amit Kumar Acharya, Ram Baran Verma
This article investigates positive supersolutions of the fully nonlinear elliptic system \[ \begin{cases} -\mathcal{M}_{λ,Λ}^{+}(D^{2}u)+|\nabla u|^{q} \geqλ_{1}f_{1}(v)~~\text{in}…
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…
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…
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…
The Second Law as a constraint and admitting the approximate nature of constitutive assumptions
Amit Acharya
A scheme for treating the Second Law of thermodynamics as a constraint and accounting for the approximate nature of constitutive assumptions in continuum thermomechanics is discuss…
Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants
N. Sukumar, Amit Acharya
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do…
Variational Dual Solutions of Chern-Simons Theory
Amit Acharya, Janusz Ginster, Ambar N. Sengupta
A scheme for generating weakly lower semi-continuous action functionals corresponding to the Euler-Lagrange equations of Chern-Simons theory is described. Coercivity is deduced for…
Ideal Magnetohydrodynamics and Field Dislocation Mechanics
Amit Acharya
The fully nonlinear (geometric and material) system of Field Dislocation Mechanics is reviewed to establish an exact analogy with the equations of ideal magnetohydrodynamics (ideal…
A Hidden Convexity of Nonlinear Elasticity
Siddharth Singh, Janusz Ginster, Amit Acharya
A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notion…
Variational principle for a damped, quadratically interacting particle chain with nonconservative forcing
Amit Acharya, Ambar N. Sengupta
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features…