Hi, i am trying to find greens function for the heat equation with a=1, i.e du/dt - d2u/dx2 = f(x,t) for 0<x<infinty i also have the conditions, u(x,0)=0 and u(0,t)=0
When i have found my greens function i have to allow f(x,t) = delta(x-1) delta(t-1) and obtain a solution using the greens...
I have the non linear pde
du/dt = d/dx [3 u^2 - d^2u/dx^2]
the question supposes that there is a solution u(x,t) = f(x-ct) where c is constant and f(y) for y=x-ct satisfies f tends to 0, f' tends to zero and f'' tends to zero but y tends to + or - infinity.
so i have tried to reduce the...
Homework Statement
my non linear pde is
du/dt = d/dx [3u2 - d2u/dx2 ]
The question says to let u(x,t) = f(x-ct)
Where the function f tends to 0, f' tends to 0 and f'' tends to 0 but the (x-ct) tends to positive or negative infinity.
Homework Equations
i thought the solution was to find...
Homework Statement
I have found the general solution to a second order pde to be
U(x,t) = f(3x + t) + g(-x + t) where f and g are arbitrary functions
I have initial conditions
U(x,0) = sin(x)
Du/dt (x,0) = cos (2x)
The Attempt at a Solution
I have found that
U(x,0) = f(3x) +...
Homework Statement
I have a pde,
16d2u/dxdy + du/dx + du/dy + au = 0 where a is constant.
Homework Equations
The Attempt at a Solution
I have tried to solve this pde using the substitutions x=e^t and y=e^s so t=ln(x) and s=ln(y) then finding
Du/dx= 1/x du/dt and du/dy= 1/y...
Homework Statement
I have a PDE for which i have found the general solution to be u(x,y) = f1(3x + t) + f2(-x + t)
where f1 and f2 are arbitrary functions. I have initial conditions u(x,0) = sin (x) and partial derivative du/dt (x,0) = cos (2x)Homework Equations
u(x,y) = f1(3x + t) + f2(-x +...
It just says what is the particle path of the flow u= (-z + cos(at)) j + (y + sin(at)) k
It is an example from a lecture, previously we had found the streamlines for the flow.
I don't understand how to find particle paths, for example i have a question that states;
u= (-z + cos(at)) j + (y + sin(at)) k
for the complementary function
y' = -z
x' = y
so y''=-y therefore y = A cos t + B sin t and z = A sin t - B cos t
Now for the particular integral, i...
is it correct that for the determinant to be one in this upper triangular matrix that the diagonal entries must also be one?
in this case will it be \prod (p ^ {i(i-1))/2}) for i = 1 to n
thank you for your patience!
can i find the formula by multiplying the number of choices for each element in the matrix together, in which case i would have p^(n(n-1)/2)p^n choices for each matrix then the product of this over all matrices would be the formula.
i hope I am not too wrong here...