One-dimensional conservation law with boundary conditions: general results and spatially inhomogeneous case
Abstract
The note presents the results of the recent work \cite{AS-Tran} of K. Sbihi and the author on existence and uniqueness of entropy solutions for boundary-value problem for conservation law $u_t+\ph(u)_x=0$ (here, we focus on the simplified one-dimensional setting). Then, using nonlinear semigroup theory, we extend these well-posedness results to the case of spatially dependent flux $\ph(x,u)$.
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