In this paper we prove a new chain rule formula for the distributional derivative of the composite function ν(x) = B(x, u(x)), where u : ]a, b[ → ℝd has bounded variation, B(x, ·) is continuously differentiable, and B(·, u) has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space variable. Copyright © 2011 by SIAM.
A chain rule formula in the space BV and applications to conservation laws / Crasta, Graziano; DE CICCO, Virginia. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 43:1(2011), pp. 430-456. [10.1137/100804462]
A chain rule formula in the space BV and applications to conservation laws
CRASTA, Graziano;DE CICCO, Virginia
2011
Abstract
In this paper we prove a new chain rule formula for the distributional derivative of the composite function ν(x) = B(x, u(x)), where u : ]a, b[ → ℝd has bounded variation, B(x, ·) is continuously differentiable, and B(·, u) has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space variable. Copyright © 2011 by SIAM.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
