Adjoint methods for static Hamilton–Jacobi equations
By Hung Vinh Tran. 2009
59 citations recorded by the source corpus.
We use the adjoint methods to study the static Hamilton–Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of regularized equations of vanishing viscosity type, and from the solutions σε of those we can get the properties of the solutions u of the Hamilton–Jacobi equations. We classify the static equations into two types and present two new ways to deal with each type. The methods can be applied to various static problems and point out the new ways to look at those PDE.
Subfields: Computational Theory and Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/143ac26533856e5c9b8caf99ee9f4c67e47900c1
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In Computational Theory and Mathematics
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- Selection problems for a discount degenerate viscous Hamilton–Jacobi equation (2017, methodology): “See [12, 32, 7, 6] for instance.”
- A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians (2012, unknown): “[15] H. Mitake, H. V. Tran, Remarks on the large-time behavior of viscosity solutions of quasi- monotone weakly coupled systems of Hamilton–Jacobi equations, Asymptot.”