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In this paper we study the Ostrovsky-Hunter equation for the case where theflux function $f(x, u)$ may depend on the spatial variable with certainsmoothness. Our main results are that if the flux function is smooth enough(specified later), then there exists a unique entropy solution. To show theexistence, after proving some a priori estimates we have used the method ofcompensated compactness and to prove the uniqueness we have employed the methodof doubling of variables.

Well-posedness of the initial value problem for the Ostrovsky-Hunter equation with spatially dependent flux