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  "body": "\n## Summary\n\nAn integro-partial differential equation is an equation for an unknown function of several variables.\nIt involves both partial derivatives of the function and integrals of it.\nIt combines a [[partial differential equation|GC5BDZ6QBC]] with integral terms, which typically describe nonlocal interactions in space or memory in time.\nMain examples are the [[Boltzmann equation|MH6CSWD7F0]] of gas dynamics, the [[radiative transfer equation|EX9YYRMAJA]], [[population balance equations|6Q7H2FQ12Q]] and nonlocal diffusion equations.\nTheir analysis mixes PDE methods with the theory of integral operators.\n\n## Explanations\n\n### L1 human\n\nIn the heat equation, heat at a point flows only to nearby points, which is a statement about derivatives.\nIn a nonlocal model, heat can jump from a point to any other point, with a rate that depends on the distance.\nThen the change in time is given by an integral over all other points, and the equation contains both a time derivative and a space integral.\nFor example, $\\partial_t u(x, t) = \\int_{\\R} J(x - y) \\big(u(y, t) - u(x, t)\\big) \\, dy$ is such a nonlocal diffusion equation.\n",
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