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APM346-2021S => APM346--Tests & Quizzes => Quiz 1 => Topic started by: Jiaqi Bi on January 28, 2021, 12:26:19 PM

Title: Quiz 1-0201 C Problem 1
Post by: Jiaqi Bi on January 28, 2021, 12:26:19 PM
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 $u_x$.