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- W2769767865 abstract "Abstract We investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mi>ε</m:mi> <m:mrow> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:msub> <m:mi>H</m:mi> <m:msub> <m:mi>x</m:mi> <m:mn>2</m:mn> </m:msub> </m:msub> <m:mo>,</m:mo> <m:mrow> <m:mo>-</m:mo> <m:msub> <m:mi>H</m:mi> <m:msub> <m:mi>x</m:mi> <m:mn>1</m:mn> </m:msub> </m:msub> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {{varepsilon}^{-1}(H_{x_{2}},-H_{x_{1}})} of a Hamiltonian H , with <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>ε</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {{varepsilon}>0} . We establish the convergence, as <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>ε</m:mi> <m:mo>→</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>+</m:mo> </m:mrow> </m:mrow> </m:math> {{varepsilon}to 0+} , of solutions of the Hamilton–Jacobi equations and identify the limit of the solutions as the solution of systems of ordinary differential equations on a graph. This result generalizes the previous one obtained by the author to the case where the Hamiltonian H admits a degenerate critical point and, as a consequence, the graph may have more than four segments at a node." @default.
- W2769767865 created "2017-12-04" @default.
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- W2769767865 date "2017-11-14" @default.
- W2769767865 modified "2023-09-24" @default.
- W2769767865 title "An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms" @default.
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- W2769767865 doi "https://doi.org/10.1515/acv-2017-0046" @default.
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