THE CONTROL OF THE BLOWING-UP TIME FOR THE SOLUTION OF THE SEMILINEAR PARABOLIC EQUATION WITH IMPULSIVE EFFECT

  • Bainov, Drumi-D (Medical University of Sofia) ;
  • Dimitar A.Kolev (Department of Mathematics, University of chemical Technology and Metallurgy) ;
  • Kiyokaza Nakagawa (Department of Mathematics Tohoku Gakuin University)
  • Published : 2000.09.01

Abstract

An impulsive semilinear parabolic equation subject to Robin boundary condition is considered. We prove that for certain classes of impulsive sources and continuous initial data, the solutions of the problem under consideration blow up in the desired time interval.

References

  1. Nonlin. World v.3 Trends in the theory of impulsive partial differential equations D. Bainov;E. Minchev
  2. Approximate Solutions of Impulsive Hyperbolic Equations D. Bainov;Zd. Kamont;E. Minchev
  3. Proceedings of Dynamical Systems and Applications v.1 Effects of degenerate parabolic operators on quenching and beyond quenching C. Y. Chan;P. C. Kong
  4. Nonlinear Analysis v.22 Impulsive quenching for reaction-diffusion equations C. Y. Chan;L. Ke;A. S. Vatsala
  5. J. Austral. Math. Soc. Ser. B v.32 Comparison principle for impulsive parabolic equations with applications to models of single species growth L. H. Erbe;H. I. Freedman;X. Z. Liu;J. H. Wu
  6. Indiana Univ. Math. J. v.34 Blow-up of positive solutions of heat equations A. Friedman;B. McLeod
  7. Nonlinear Analysis, Theory, Methods and Applications v.28 no.2 Comparison results for systems of impulse parabolic equations with applicatiosn to population dynamics M. Kirane;Y. V. Rogovchenko
  8. Proceedings of 8th Int. Coll. on Differential Equations Asymptotic Behaviour of Solutions of an Impulsive Semilinear Parabolic Cauchy Problem K. Nakagawa;D. Bainov(Ed.)
  9. Nonlinear Parabolic and Elliptic Equations C. V. Pao
  10. Linear and Nonlinear Waves G. B. Whitham