APM346-2021S > Quiz 1

Quiz 1-0201 C Problem 1

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Jiaqi Bi:
Problem 1: Determine if they are linear homogeneous, linear inhomogeneous, or nonlinear ($u$ is an unknown function); for nonlinear equations, indicate if they are also semilinear, or quasilinear:
$$u_t+xu_x=0$$
Solution:
This is linear homogeneous because it has $f(x)=0$ on the RHS, and $Lu$ is a partial differential expression linear, such that it contains only coefficient $1$ and $x$ for $u_t$ and $u_x$.