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Application of accretive operators theory to evolutive combined conduction, convection and radiation.

María Michaela Porzio, Oscar López-Pouso (2004)

Revista Matemática Iberoamericana

The accretive operators theory is employed for proving an existence theorem for the evolutive energy equations involving simultaneously conduction, stationary convection (in the sense that the velocity field is assumed to be time independent), and radiation. In doing that we need to use new existence results for elliptic linear problems with mixed boundary conditions and irregular data.

Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on m -tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations

Eva Brestovanská, Milan Medveď (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the m -tuple Cartesian product of a Banach algebra X over . Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.

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