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Weak versus D-solutions to linear hyperbolic first order systems with constant coefficients

Katzourakis, N. (2018) Weak versus D-solutions to linear hyperbolic first order systems with constant coefficients. Journal of Hyperbolic Differential Equations, 15 (2). pp. 329-347. ISSN 1793-6993

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To link to this item DOI: 10.1142/S0219891618500121

Abstract/Summary

We establish a consistency result by comparing two independent notions of generalized solutions to a large class of linear hyperbolic first-order PDE systems with constant coefficients, showing that they eventually coincide. The first is the usual notion of weak solutions defined via duality. The second is the new notion of D-solutions which we recently introduced and arose in connection to the vectorial calculus of variations in L∞ and fully nonlinear elliptic systems. This new approach is a duality-free alternative to distributions and is based on the probabilistic representation of limits of difference quotients.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:75142
Publisher:World Scientific Publishing Co Pte Ltd

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