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Abstrakty
In the paper the Cauchy problem for and infinite system of parabolic type equations is studied. The general operators of the parabolic type of second order with variable coefficients are considered and the system is weakly coupled. Among the obtained results there is a theorem on differential inequality as well as the existence and uniqueness theorem in the class of continuous-bounded functions obtained by monotone iterative method.
Czasopismo
Rocznik
Tom
Strony
307--318
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland, fronczyk@wms.mat.agh.edu.pl
Bibliografia
- [1] Appell J., Zabrejko P.P.: Nonlinear Superposition Operators. Cambridge, Cambridge University Press 1990.
- [2] Benilan Ph., Wrzosek D.: On an infinite systems of reaction-diffusion equations. Adv. Math. Sci. Appl. 7 (1997).
- [3] Brzychczy S.: Some variant of iteration method for infinite systems of parabolic differential-functional equations. Opuscula Math. 20 (2002).
- [4] Brzychczy S.: Existence and Uniqueness of Solutions of Infinite Systems of Se-milinear Parabolic Differential-Functional Equations in Arbitrary Domains in Ordered Banach Spaces. Math. Comput. Modelling 36 (2002).
- [5] Bychowska A., Leszczyński H.: Comparison principles for parabolic differential-functional initial-value problems. Nonlinear Anal. 57 (2004).
- [6] Dolgosheina E. B., Karulin A.Yu., Bobylev A.V.: A kinetic model of the agglutination process. Math. Biosciences 109 (1992).
- [7] Drake R.: A general mathematical survey of the coagulation equation. In: Topics in Currant Aerosol Research, Hidy G. M., Brock J. R. [eds.], Pergamon Press, Oxford 1972.
- [8] Eidel'man S.D.: Parabolic Systems. North-Holland, 1969.
- [9] Ernst M.H., Ziff R. M., Hendriks E. M.: Coagulation processes with phase transition. J. Colloid Interface Sci. 97 (1984).
- [10] Friedman A.: Partial Differential Equations of Parabolic Type. Englewood Cliffs, New Jersey, Prentice-Hall, Inc. 1964.
- [11] Hendriks E.M., Ernst M.H., Ziff R. M.: Coagulation equations with gelation J. Statist. Phys. 31 (1983).
- [12] Ladde G. S., Lakshmikantham V., Vatsala A. S.: Monotone Iterative Techniques for Nonlinear Differential Equations. Boston, MA, Pitman (1985).
- [13] Pao C. V.: Nonlinear Parabolic and Elliptic Equations. New York, Plenum Press (1992).
- [14] Perelson A., Samsel R.: Kinetics of red blood cell aggregation: an example of geometric polymerization In: Kinetics of Aggregation and Gelation, Family F., Landau D.P. (Eds.), Amsterdam, Elsevier Science Publ., 1984.
- [15] Pudełko A.: Existence and uniqueness of solutions Cauchy problem for nonlinear infinite systems of parabolic differential-functional equations. Acta Math. Univ. Iagel. 40 (2002).
- [16] Safronov V. S.: Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets. Israel Program for Scientific Translations Ltd., 1972.
- [17] Smoluchowski M.: Versuch einer mathematischen Theorie der kolloiden Lósun-gen. Z. Phys. Chem. 92 (1917).
- [18] Szarski J.: Differential Inequalities. Monografie Matematyczne 43, Warszawa, PWN (1965).
- [19] Walter W.: Differential and Integral Inequalities. Berlin, Springer 1970.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0003-0053