Discontinuous solutions of $U_t + H(U_x) = 0$ versus measure-valued solutions of $u_t + [H(u)]_x = 0$

Alberto Tesei

doi:10.4171/rlm/941

JournalsrlmVol. 32, No. 3pp. 391–411

Discontinuous solutions of $U_{t} + H (U_{x}) = 0$ versus measure-valued solutions of $u_{t} + [H (u)]_{x} = 0$

Alberto Tesei
Università di Roma La Sapienza; Istituto per le Applicazioni del Calcolo ‘‘M. Picone’’, CNR, Roma, Italy

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Abstract

Let $H$ be a bounded Lipschitz continuous function. We discuss some recent results concerning discontinuous viscosity solutions of the Hamilton–Jacobi equation $U_{t} + H (U_{x}) = 0$ 0, signed Radon measure-valued entropy solutions of the conservation law $u_{t} + [H (u)]_{x} = 0$ , and their connection.

Cite this article

Alberto Tesei, Discontinuous solutions of $U_{t} + H (U_{x}) = 0$ versus measure-valued solutions of $u_{t} + [H (u)]_{x} = 0$ . Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 3, pp. 391–411

DOI 10.4171/RLM/941