Theoretical and Mathematical Physics

, Volume 201, Issue 1, pp 1457–1467 | Cite as

Blowup Solutions of the Nonlinear Thomas Equation

  • M. O. KorpusovEmail author


We study boundary value problems on an interval and on the half-line for the well-known Thomas equation uxt + αux + βut + uxut = 0, which is a model equation describing processes in chemical kinetics with ion exchange during sorption in a reagent stream. For this equation, we obtain sufficient conditions for its solution blowup in a finite time.


Sobolev-type nonlinear equation blowup local solvability nonlinear capacity blowup time estimate 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Conflicts of interest. The author declares no conflicts of interest.


  1. 1.
    H. C. Thomas, “Heterogeneous ion exchange in a flowing system,” J. Am. Chem. Soc., 66, 1664–1666 (1944).CrossRefGoogle Scholar
  2. 2.
    R. R. Rosales, “Exact solutions of some nonlinear evolution equations,” Stud. Appl. Math., 59, 117–151 (1978).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    A. R. Chowdhury and S. Paul, “Lax pair, Lie–Backlund symmetry, and hereditary operator for the Thompson equation,” Phys. Scr., 30, 9 (1984).ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    W. T. Wong and P. C. W. Fung, “Prolongation structure for the Thompson equation,” Nuovo Cimento B, 99, 163–170 (1987).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    S. Y. Sakovich, “On the Thomas equation,” J. Phys. A: Math. Gen., 21, L1123–L1126 (1988).ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    G. M. Wei, Y. T. Gao, and H. Zhang, “On the Thomas equation for the ion-exchange operations,” Czech. J. Phys., 52, 749–751 (2002).ADSCrossRefGoogle Scholar
  7. 7.
    E. Mitidieri and S. I. Pokhozhaev, “A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities,” Proc. Steklov Inst. Math., 234, 1–362 (2001).zbMATHGoogle Scholar
  8. 8.
    V. A. Ditkin and A. P. Prudnikov, Handbook of Operational Calculus [in Russian], Moscow, Vysshaya Shkola (1965).zbMATHGoogle Scholar
  9. 9.
    F. G. Tricomi, Lezioni sulle equazioni a derivate parziali (Italian Corso di analisi superiore, anno accademico 1953-1954), Editrice Gheroni, Torino (1954).zbMATHGoogle Scholar
  10. 10.
    G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge (1944).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations