Linear partial differential equation of first order
Answers
Answered by
0
Definition
First order PDE in two independent variables is a relation
F(x, y; u; ux, uy) = 0
F a known real function from D3 ⊂ R
5 → R
(1)
Examples: Linear, semilinear, quasilinear, nonlinear equations -
ux + uy = 0
ux + uy = ku, c and k are constant
ux + uy = u
2
uux + uy = 0
u
2
x − u
2
y = 0
u
2
x + u
2
y + 1 = 0
ux +
q
1 − u
2
y = 0, defined for |uy| ≤ 1 (2)
A Model Lession FD PDE Part 1 P. Prasad Department of Mathematics 2 / 50
First order PDE in two independent variables is a relation
F(x, y; u; ux, uy) = 0
F a known real function from D3 ⊂ R
5 → R
(1)
Examples: Linear, semilinear, quasilinear, nonlinear equations -
ux + uy = 0
ux + uy = ku, c and k are constant
ux + uy = u
2
uux + uy = 0
u
2
x − u
2
y = 0
u
2
x + u
2
y + 1 = 0
ux +
q
1 − u
2
y = 0, defined for |uy| ≤ 1 (2)
A Model Lession FD PDE Part 1 P. Prasad Department of Mathematics 2 / 50
Similar questions