 Existence, uniqueness and blow-up of solutions for generalized auto-convolution Volterra integral equationsMahdi Mostafazadeh, Sedaghat Shahmorad and Fevzi Erdoğan Applied Mathematics and Computation, 2024, vol. 471, issue C Abstract: In this paper, our intention is to investigate the blow-up theory for generalized auto-convolution Volterra integral equations (AVIEs). To accomplish this, we will consider certain conditions on the main equation. This will establish a framework for our analysis, ensuring that the solution of the equation exists uniquely and is positive. Firstly, we analyze the existence and uniqueness of a local solution for a more general class of AVIEs (including the proposed equation in this paper) under certain hypotheses. Subsequently, we demonstrate the conditions under which this local solution blows up at a finite time. In other words, the solution becomes unbounded at that time. Furthermore, we establish that this blow-up solution can be extended to an arbitrary interval on the non-negative real line, thus referred to as a global solution. These results are also discussed for a special case of generalized AVIEs in which the kernel functions are taken as positive constants. Keywords: Auto-convolution; Finite-time blow-up; Volterra integral equation; Existence; Uniqueness (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:471:y:2024:i:c:s0096300324000808 DOI: 10.1016/j.amc.2024.128608 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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