Mostafazadeh, MahdiShahmorad, SedaghatErdogan, Fevzi2025-05-102025-05-1020240096-30031873-564910.1016/j.amc.2024.1286082-s2.0-85185202197https://doi.org/10.1016/j.amc.2024.128608https://hdl.handle.net/20.500.14720/10891In 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.eninfo:eu-repo/semantics/closedAccessAuto-ConvolutionFinite-Time Blow-UpVolterra Integral EquationExistenceUniquenessArticle471Q1Q1WOS:001187950700001