Glasnik Matematicki, Vol. 38, No.2 (2003), 359-376.

THE EXPECTATION OF SOLUTION OF RANDOM CONTINUITY EQUATION WITH GAUSSIAN VELOCITY FIELD

Zoran Pasarić

Center for Marine and Enviromental Research, Rudjer Boskovic Institute, Bijenicka cesta 54, 10000 Zagreb, Croatia
Geophysical Institute, Faculty of Science, University of Zagreb, Horvatovac bb, 10000 Zagreb, Croatia
e-mail: pasaric@rudjer.irb.hr


Abstract.   The continuity equation in d-dimensional space with random velocity field defined by means of a vector-valued Gaussian process is studied. The expectation of corresponding evolution family of operators is explicitly derived, generalizing in a sense the evolution family corresponding to the conventional diffusion equation.

2000 Mathematics Subject Classification.   46N20, 47B44, 60H25.

Key words and phrases.   Random transport equation.


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