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Blowup Solutions of the Nonlinear Thomas Equation

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Abstract

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.

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References

  1. H. C. Thomas, “Heterogeneous ion exchange in a flowing system,” J. Am. Chem. Soc., 66, 1664–1666 (1944).

    Article  Google Scholar 

  2. R. R. Rosales, “Exact solutions of some nonlinear evolution equations,” Stud. Appl. Math., 59, 117–151 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  3. A. R. Chowdhury and S. Paul, “Lax pair, Lie–Backlund symmetry, and hereditary operator for the Thompson equation,” Phys. Scr., 30, 9 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  4. W. T. Wong and P. C. W. Fung, “Prolongation structure for the Thompson equation,” Nuovo Cimento B, 99, 163–170 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  5. S. Y. Sakovich, “On the Thomas equation,” J. Phys. A: Math. Gen., 21, L1123–L1126 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    MATH  Google Scholar 

  8. V. A. Ditkin and A. P. Prudnikov, Handbook of Operational Calculus [in Russian], Moscow, Vysshaya Shkola (1965).

    MATH  Google Scholar 

  9. F. G. Tricomi, Lezioni sulle equazioni a derivate parziali (Italian Corso di analisi superiore, anno accademico 1953-1954), Editrice Gheroni, Torino (1954).

    MATH  Google Scholar 

  10. G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge (1944).

    MATH  Google Scholar 

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Correspondence to M. O. Korpusov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 1, pp. 54–64, October, 2019.

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Korpusov, M.O. Blowup Solutions of the Nonlinear Thomas Equation. Theor Math Phys 201, 1457–1467 (2019). https://doi.org/10.1134/S0040577919100040

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  • DOI: https://doi.org/10.1134/S0040577919100040

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