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

Stanisław Brzychczy

Annales Polonici Mathematici (1999)

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

Abstract

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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.

How to cite

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Brzychczy, 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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  1. [1] J. Appell and P. P. Zabrejko, Nonlinear Superposition Operators, Cambridge Univ. Press, Cambridge, 1990. 
  2. [2] P. Bénilan and D. Wrzosek, On an infinite system of reaction-diffusion equations, Adv. Math. Sci. Appl. 7 (1997), 349-364. 
  3. [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. [4] S. Brzychczy, Monotone Iterative Methods for Nonlinear Parabolic and Elliptic Differential-Functional Equations, Dissertations Monographs, 20, Wyd. AGH, Kraków, 1995. Zbl0843.35129
  5. [5] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, 1964. Zbl0144.34903
  6. [6] M. Lachowicz and D. Wrzosek, A nonlocal coagulation-fragmentation model, Appl. Math. (Warsaw), to appear. 
  7. [7] M. Smoluchowski, Versuch einer mathematischen Theorie der kolloiden Lösungen, Z. Phys. Chem. 92 (1917), 129-168. 
  8. [8] J. Szarski, Differential Inequalities, Monografie Mat. 43, PWN, Warszawa, 1965. 
  9. [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. [10] J. Szarski, Infinite systems of parabolic differential-functional inequalities, ibid. 28 (1980), 477-481. Zbl0503.35044

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