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Some surjectivity theorems with applications

H. K. PathakS. N. Mishra — 2013

Archivum Mathematicum

In this paper a new class of mappings, known as locally λ -strongly φ -accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ -accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ -strongly φ -accretive mappings by using Caristi-Kirk fixed point theorem. In the sequel, we introduce the notion...

Convergence of Vanishing Viscosity Approximations of 2 x 2 Triangular Systems of Multi-Dimensional Conservation Laws

G. M. CocliteK. H. KarlsenS. MishraN. H. Risebro — 2009

Bollettino dell'Unione Matematica Italiana

We consider a multidimensional triangular system of conservation laws. These equations arise in models of three phase flows in porous media and include multi dimensional conservation laws with discontinuous coefficients as special cases. We study approximate solutions of these equations constructed by the vanishing viscosity method and show that the approximate solutions converge to a weak solution of the multi-dimensional triangular system.

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