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  "body": "\n## Summary\n\nA semilinear PDE is a [[partial differential equation|GC5BDZ6QBC]] whose highest-order part is linear with coefficients depending only on the variables.\nIts lower-order terms may be nonlinear.\nThe principal part, which decides the type of the equation, is then the same as for a linear equation.\nMany models of physics and biology have this form, such as reaction–diffusion equations and nonlinear wave equations.\nSee the [[definition|X3P4TQZ9X2]].\n\n## Explanations\n\n### L1 human\n\nThink of a linear equation such as the heat equation, and add a nonlinear source term that depends on the unknown itself.\nFor example, $\\partial_t u = \\partial_x^2 u + u(1 - u)$ is [[Fisher's equation|AXV2PH7FEZ]].\nThe second derivatives enter linearly, but the term $u(1 - u)$ does not.\nBecause the highest derivatives behave as in a linear equation, much of the linear theory still applies.\n",
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