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On Hyperbolic Variational Inequalities of First Order and Some Applications

In: Nonlinear Differential Equation Models

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  • José Francisco Rodrigues

    (Universidade de Lisboa, CMAF)

Abstract

This paper presents further developments in the study of strong solutions and their coincidence sets to the obstacle problem for linear transport operators. Under natural mild assumptions, the strong convergence of the solutions and the characteristic functions of their coincidence sets is obtained in the passage of second order to first order problems. An application to a steady-state chemotaxis problem is given. The extension to the two obstacles problem of first order is also presented, having in view an application to a porous media model in presence of saturation arising in petroleum engineering.

Suggested Citation

  • José Francisco Rodrigues, 2004. "On Hyperbolic Variational Inequalities of First Order and Some Applications," Springer Books, in: Ansgar Jüngel & Raul Manasevich & Peter A. Markowich & Henrik Shahgholian (ed.), Nonlinear Differential Equation Models, pages 157-177, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0609-9_12
    DOI: 10.1007/978-3-7091-0609-9_12
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