The Ostrovsky Hunter equation with a space dependent flux function
Provides theoretical guarantees for a class of nonlinear PDEs with spatially varying coefficients, relevant to mathematical physics and numerical analysis.
The paper establishes existence and uniqueness of entropy solutions for the periodic Ostrovsky-Hunter equation with a space-dependent flux function, and proves that a finite volume scheme converges at rate 1/2.
We study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution. This entropy solution may be constructed as a limit of approximate solutions generated by a finite volume scheme, and the finite volume approximations converge to the entropy solution at a rate 1/2.