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Hamilton–Jacobi Equations

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A Basic Guide to Uniqueness Problems for Evolutionary Differential Equations

Part of the book series: Compact Textbooks in Mathematics ((CTM))

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Abstract

In the last chapter, we discussed uniqueness in a special class of weak solutions called entropy solutions for scalar conservation laws, which are quasilinear first-order equations. The notion of a weak solution and an entropy solution is based on integration by parts or a variational principle.

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Notes

  1. 1.

    For a subset A in a metric space M equipped with distance d, the distance function \(\operatorname {dist}(x,A)\) from A is defined by

    $$\displaystyle \begin{aligned} \operatorname{dist}(x,A):=\inf\left\{d(x,y)\bigm|y\in A\right\}.\end{aligned}$$

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan

    Mi-Ho Giga & Yoshikazu Giga

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  1. Mi-Ho Giga
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  2. Yoshikazu Giga
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Giga, MH., Giga, Y. (2023). Hamilton–Jacobi Equations. In: A Basic Guide to Uniqueness Problems for Evolutionary Differential Equations. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-34796-2_4

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