Geodesic
Existence of solutions for infinite systems of parabolic equations with functional dependence
Anna Pude/lko1
1 Faculty of Applied Mathematics AGH University of Science and Technology Al. Mickiewicza 30 30-059 Kraków, Poland
Annales Polonici Mathematici, Tome 86 (2005) no. 2, pp. 123-135

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method.
DOI : 10.4064/ap86-2-3
Keywords: cauchy problem infinite system parabolic type equations studied general operators parabolic type second order variable coefficients considered system weakly coupled prove existence uniqueness bounded solution under carath odory type conditions its differentiability existence uniqueness class functions satisfying natural growth condition results obtained fixed point method

Anna Pude/lko 1

1 Faculty of Applied Mathematics AGH University of Science and Technology Al. Mickiewicza 30 30-059 Kraków, Poland 
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Anna Pude/lko. Existence of solutions for infinite systems of parabolic
 equations with functional dependence. Annales Polonici Mathematici, Tome 86 (2005) no. 2, pp. 123-135. doi: 10.4064/ap86-2-3

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