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Remarks on coupled Abel type integral equations. (English) Zbl 1469.45003

The paper is concerned with the existence and the blow-up of positive solutions to a system of nonlinear Volterra integral equations of Abel type arising in the modeling of combustion processes. The author simplifies and generalizes two of his earlier related studies, namely [Colloq. Math. 146, No. 1, 99–110 (2017; Zbl 1362.45011); J. Integral Equations Appl. 30, No. 1, 147–166 (2018; Zbl 1404.45010)].

MSC:

45D05 Volterra integral equations
45G10 Other nonlinear integral equations
45G15 Systems of nonlinear integral equations
45M20 Positive solutions of integral equations
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References:

[1] G. Gripenberg, S. O. Londen and O. Staffans,Volterra Integral and Functional Equations, Encyclopedia Math. Appl. 34, Cambridge Univ. Press, New York, 1990. · Zbl 0695.45002
[2] D. G. Lasseigne and W. E. Olmstead,Ignition or nonignition of a combustible solid with marginal heating, Quart. Appl. Math. 49 (1991), 303-312. · Zbl 0731.76039
[3] W. Mydlarczyk,A system of Volterra integral equations with blowing up solutions, Colloq. Math. 146 (2017), 99-110. · Zbl 1362.45011
[4] W. Mydlarczyk,Coupled Volterra integral equations with blow up solutions, J. Integral Equations Appl. 30 (2018), 147-166. · Zbl 1404.45010
[5] W. Mydlarczyk and W. Okrasiński,A nonlinear system of Volterra integral equations with convolution kernels, Dynam. Systems Appl. 14 (2005), 111-120. · Zbl 1111.45004
[6] W. E. Olmstead, C. A. Roberts and K. Deng,Coupled Volterra equations with blow-up solutions, J. Integral Equations Appl. 7 (1995), 499-516. · Zbl 0847.45006
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