# Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations

Annales Polonici Mathematici (1999)

- Volume: 72, Issue: 1, page 15-24
- ISSN: 0066-2216

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topBrzychczy, Stanisław. "Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations." Annales Polonici Mathematici 72.1 (1999): 15-24. <http://eudml.org/doc/262721>.

@article{Brzychczy1999,

abstract = {We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.},

author = {Brzychczy, Stanisław},

journal = {Annales Polonici Mathematici},

keywords = {method of lower and upper functions; infinite systems of parabolic differential-functional equations; monotone iterative method; monotone iterative method of lower and upper functions; existence; uniqueness},

language = {eng},

number = {1},

pages = {15-24},

title = {Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations},

url = {http://eudml.org/doc/262721},

volume = {72},

year = {1999},

}

TY - JOUR

AU - Brzychczy, Stanisław

TI - Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations

JO - Annales Polonici Mathematici

PY - 1999

VL - 72

IS - 1

SP - 15

EP - 24

AB - We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.

LA - eng

KW - method of lower and upper functions; infinite systems of parabolic differential-functional equations; monotone iterative method; monotone iterative method of lower and upper functions; existence; uniqueness

UR - http://eudml.org/doc/262721

ER -

## References

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- [2] P. Bénilan and D. Wrzosek, On an infinite system of reaction-diffusion equations, Adv. Math. Sci. Appl. 7 (1997), 349-364.
- [3] S. Brzychczy, Approximate iterative method and existence of solutions of nonlinear parabolic differential-functional equations, Ann. Polon. Math. 42 (1983), 37-43. Zbl0537.35044
- [4] S. Brzychczy, Monotone Iterative Methods for Nonlinear Parabolic and Elliptic Differential-Functional Equations, Dissertations Monographs, 20, Wyd. AGH, Kraków, 1995. Zbl0843.35129
- [5] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, 1964. Zbl0144.34903
- [6] M. Lachowicz and D. Wrzosek, A nonlocal coagulation-fragmentation model, Appl. Math. (Warsaw), to appear.
- [7] M. Smoluchowski, Versuch einer mathematischen Theorie der kolloiden Lösungen, Z. Phys. Chem. 92 (1917), 129-168.
- [8] J. Szarski, Differential Inequalities, Monografie Mat. 43, PWN, Warszawa, 1965.
- [9] J. Szarski, Comparison theorem for infinite systems of parabolic differential-functional equations and strongly coupled infinite systems of parabolic equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 739-846. Zbl0461.35051
- [10] J. Szarski, Infinite systems of parabolic differential-functional inequalities, ibid. 28 (1980), 477-481. Zbl0503.35044

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