A Volterra integral equation is a type of integral equation where the unknown function appears under the integral sign and is defined over a variable limit of integration. This equation often takes the form $$u(t) = f(t) + \int_{a}^{t} K(t,s) u(s) ds$$, where $K(t,s)$ is a kernel function that depends on both variables. These equations are significant in various areas of physics and engineering, particularly in systems with memory or where the present state depends on past states.
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