APM346-2021S > Quiz 1

Quiz 1 - Variant 2E - Problem 1

(1/1)

Gavrilo Milanov Dzombeta:
Consider first order equations and 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:
$$u_t +u^2_x + u^2_y = 0.$$
$$\text{The equation is nonlinear homogeneous}$$

Victor Ivrii:
Indeed, this equation has $u=0$ as a solution but the notion of "homogeneou"s does not apply to nonlinear.

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