Journal of Integral Equations and Applications

Coupled Volterra integral equations with blowing up solutions

Wojciech Mydlarczyk

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Abstract

In this paper, a system of nonlinear integral equations related to combustion problems is considered. Necessary and sufficient conditions for the existence and explosion of positive solutions are given. In addition, the uniqueness of the positive solutions is shown. The main results are obtained by monotonicity methods.

Article information

Source
J. Integral Equations Applications, Volume 30, Number 1 (2018), 147-166.

Dates
First available in Project Euclid: 10 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1523347342

Digital Object Identifier
doi:10.1216/JIE-2018-30-1-147

Mathematical Reviews number (MathSciNet)
MR3784886

Zentralblatt MATH identifier
06873402

Subjects
Primary: 45D05: Volterra integral equations [See also 34A12]
Secondary: 45G10: Other nonlinear integral equations 45M20: Positive solutions

Keywords
System of nonlinear Volterra integral equations existence of nontrivial solutions blowing-up solution

Citation

Mydlarczyk, Wojciech. Coupled Volterra integral equations with blowing up solutions. J. Integral Equations Applications 30 (2018), no. 1, 147--166. doi:10.1216/JIE-2018-30-1-147. https://projecteuclid.org/euclid.jiea/1523347342


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References

  • P.J. Bushell and W. Okrasiński, Nonlinear Volterra equations and the Apéry identities, Bull. Lond. Math. Soc. 24 (1992), 478–484.
  • ––––, On the maximal interval of existence for solutions to some nonlinear Volterra integral equations with convolution kernel, Bull. Lond. Math. Soc. 28 (1996), 59–65.
  • G. Gripenberg, Unique solutions of some Volterra integral equations, Math. Scand. 48 (1981), 59–67.
  • G. Gripenberg, S.O. Londen and O. Staffans, Volterra integral and functional equations, Encycl. Math. Appl. 34, Cambridge University Press, New York, 1990.
  • D.G. Lasseigne and W.E. Olmstead, Ignition or nonignition of a combustible solid with marginal heating, Quart. Appl. Math. 49 (1991), 303–312.
  • W. Mydlarczyk, Remark on nonlinear Volterra equations, Ann. Polon. Math. 53 (1991), 227–232.
  • ––––, The existence of nontrivial solutions of Volterra equations, Math. Scand. 68 (1991), 83–88.
  • ––––, A condition for finite blow-up time for a Volterra equations, J. Math. Anal. Appl. 181 (1994), 248–253.
  • ––––, A system of Volterra integral equations with blowing up solutions, Colloq. Math. 146 (2017), 99–110.
  • W. Mydlarczyk and W. Okrasiński, A nonlinear system of Volterra integral equations with convolution kernels, Dyn. Syst. Appl. 14 (2005), 111–120.
  • W. Mydlarczyk, W. Okrasiński and C. Roberts, Blow-up solutions to a system of nonlinear Volterra integral equations, J. Math. Anal. Appl. 301 (2005), 208–218.
  • W. Okrasiński, Nontrivial solutions to nonlinear Volterra integral equations, SIAM J. Math. Anal. 11 (1991), 1007–1015.
  • W.E. Olmstead, C.A. Roberts and K. Deng, Coupled Volterra equations with blow-up solutions, J. Integral Eqs. Appl. 7 (1995), 499–516.
  • C.A. Roberts, Analysis of explosion for nonlinear Volterra equations with blow-up solutions, J. Comp. Appl. Math. 97 (1998), 153–166.
  • C.A. Roberts, D.G. Lasseigne and W.E. Olmstead, Volterra equations which models explosion in a diffusive medium, J. Intgeral Eqs. Appl. 5 (1993), 531–546.