- #1

chwala

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- Homework Statement
- This is my own question - set by me

- Relevant Equations
- Pde

Solve the given PDE for ##u(x,t)##;

##\dfrac{∂u}{∂t} +8 \dfrac{∂u}{∂x} = 0##

##u(x,0)= \sin x##

##-∞ <x<∞ , t>0##

In my working (using the method of characteristics) i have,

##x_t =8##

##x(t) = 8t + a##

##a = x(t) - 8t## being the first characteristic.

For the second characteristic,

##u(x(t),t) = f(a) = \sin a = \sin (x(t)-8t)##

thus the solution is,

##u(x,t) = \sin (x-8t)##

Insight welcome. Cheers.

##\dfrac{∂u}{∂t} +8 \dfrac{∂u}{∂x} = 0##

##u(x,0)= \sin x##

##-∞ <x<∞ , t>0##

In my working (using the method of characteristics) i have,

##x_t =8##

##x(t) = 8t + a##

##a = x(t) - 8t## being the first characteristic.

For the second characteristic,

##u(x(t),t) = f(a) = \sin a = \sin (x(t)-8t)##

thus the solution is,

##u(x,t) = \sin (x-8t)##

Insight welcome. Cheers.

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