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We extend the notion of H-measures on test functions defined on IRd × P , where P ⊂ IRd is an arbitrary compact simply connected Lipschitz manifold such that there exists a family of regular nonintersecting curves issuing from the manifold and fibrating IRd. We introduce a concept of quasisolutions to purely fractional scalar conservation laws and apply our… (More)
1. Notations. The following notation will be used: 93: a complex Banach algebra with elements x, y, • ■ • , a unit element e and a norm ||x|| of x£93; 93*: the adjoint of 93; 93o: the subalgebra of S3 defined by 93o = e3, where g is the field of complex numbers; 6: the zero element of 93; L: a simple closed smooth positively oriented curve decomposing the… (More)
We prove that a sequence of quasi-solutions to non-degenerate degenerate parabolic equations with rough coefficients is strongly Lloc-precompact. The result is obtained using the H-measures and a new concept of quasihomogeneity. A consequence of the precompactness is existence of a weak solution to the equation under consideration.