= Semilinear partial differential equation
A semilinear partial differential equation is linear in its highest-order derivatives, with their coefficients depending only on the independent variables; lower-order terms may depend nonlinearly on the solution and its lower derivatives. A <semilinear heat equation> such as $u_t=\Delta u+f(u)$ is an example. This differs from a quasilinear equation, whose highest-order derivative coefficients can depend on the solution or its lower derivatives.
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