Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems partial-differential-equations-by-evans · Problem 1
Nonlinear First-Order PDE
Mathematics — Calculus · transport-equation-initial-value
Problem Write down an explicit formula for a function u u u { u t + b ⋅ D u + c u = 0 in R n × ( 0 , ∞ ) u = g on R n × { t = 0 } . \begin{cases} u_t + b \cdot Du + cu = 0 & \text{in } \mathbb{R}^n \times (0,\infty) \\ u = g & \text{on } \mathbb{R}^n \times \{t=0\}. \end{cases} { u t + b ⋅ D u + c u = 0 u = g in R n × ( 0 , ∞ ) on R n × { t = 0 } . c ∈ R c \in \mathbb{R} c ∈ R b ∈ R n b \in \mathbb{R}^n b ∈ R n Browse the problem library