A spatially inhomogeneous diffusion problem with strong absorption

Riccardo Ricci; Domingo A. Tarzia

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 3, page 749-761
  • ISSN: 0392-4041

Abstract

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We study the asymptotic behaviour ( t → + ∞ ) of the solutions of a nonlinear diffusion problem with strong absorption. We prove convergence to the stationary solution in the L ∞ by means of an appropriate family of sub and supersolutions. In appendix we prove the well posedness of the problem.

How to cite

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Ricci, Riccardo, and Tarzia, Domingo A.. "A spatially inhomogeneous diffusion problem with strong absorption." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 749-761. <http://eudml.org/doc/195447>.

@article{Ricci2003,
abstract = {We study the asymptotic behaviour ($t \to +\infty$) of the solutions of a nonlinear diffusion problem with strong absorption. We prove convergence to the stationary solution in the $L^\{\infty\}$ by means of an appropriate family of sub and supersolutions. In appendix we prove the well posedness of the problem.},
author = {Ricci, Riccardo, Tarzia, Domingo A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {749-761},
publisher = {Unione Matematica Italiana},
title = {A spatially inhomogeneous diffusion problem with strong absorption},
url = {http://eudml.org/doc/195447},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Ricci, Riccardo
AU - Tarzia, Domingo A.
TI - A spatially inhomogeneous diffusion problem with strong absorption
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 749
EP - 761
AB - We study the asymptotic behaviour ($t \to +\infty$) of the solutions of a nonlinear diffusion problem with strong absorption. We prove convergence to the stationary solution in the $L^{\infty}$ by means of an appropriate family of sub and supersolutions. In appendix we prove the well posedness of the problem.
LA - eng
UR - http://eudml.org/doc/195447
ER -

References

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  1. BEREZOVSKY, A. A.- KERSNER, R., On the Stabilization and Localization of Diffusion-Reaction Processes (in Russian), in Nonlinear boundary value problems of mathematical physics and their applications, A. M. Samojlenko and A. A. Berezovsky Eds., Kiev, 1998. 
  2. BEREZOVSKY, A. A.- KERSNER, R.- PELETIER, L. A., A Free-boundary Problem for a Reaction-Diffusion Equation, preprint 
  3. BERTSCH, M., A Class of Degenerate Diffusion Equation with a singular nonlinear term, Nonlinear Anal. TMA, 7 (1983), 117-127. Zbl0509.35047MR687037
  4. COMPARINI, E.- RICCI, R.- VAZQUEZ, J. L., Asymptotic Behavior of the Solutions of a Nonlinear Fokker-Plank Equation with Dirichlet Boundary conditions, J. Math. Anal. Appl., 175 (1993), 606-631. Zbl0785.35077MR1219198
  5. DIAZ, J. I., Nonlinear Partial Differential Equations and Free Boundaries. I. Elliptic Problems, Res. Notes in Math., 106, Pitman, London (1985). Zbl0595.35100
  6. FRIEDMAN, A.- HERRERO, M. A., Extinction Properties of a Semilinear Heat Equation with Strong Absorption, J. Math. Anal. Appl., 124 (1987), 530-546. Zbl0655.35050MR887008
  7. KERSNER, R.- NICOLOSI, F., The Nonlinear Heat Equation with Absorption: Effects of Variable Coefficients, J. Math. Anal. Appl., 170 (1992), 551-566. Zbl0799.35131MR1188571
  8. LADYZENSKAJA, O. A.- SOLONNIKOV, V. A.-, N. N., , Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, vol. 23, Providence R.I., American Mathematical Society (1968). Zbl0174.15403MR241822
  9. MITROPOL'SKY, YU. A.- BEREZOVSKY, A. A., Free and Non-local Boundary Problems in Metallurgy, Medicine, Ecology and Material Sciences, Nat. Acad. Sci. Ukraine, Kiev, 2000. Zbl0894.35132
  10. RICCI, R., Large Time Behavior of the Solution of the Heat Equation with Nonlinear Strong Absorption, J. Diff. Equa., 79 (1989), 1-13. Zbl0704.35013MR997606
  11. RICCI, R.- TARZIA, D. A., Asymptotic behaviour of the Solutions of Class of Diffusion-Reaction Equations, in Free Boundary Problems: Theory and Applications, K. H. Hoffmann & J. Sprekels ed.s, Research Notes in Maths, 186 (1990), 719-721. 
  12. RICCI, R.- TARZIA, D. A., Asymptotic Behavior of the solution of the solution of the dead-core problem, Nonlinear Anal. T.M.A., 13 (1989), 405-411. Zbl0699.35022MR987377
  13. STAKGOLD, I., Reaction-diffusion problem in chemical engineering, in «Nonlinear Diffusion Problem» (A. Fasano and M. Primicerio, Eds.), Lect. Notes in Math., 1224, Springer-Verlag, Berlin, 1986. Zbl0637.76090

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