Recent content by somethingstra

I've read that many times and still do not understand. Can someone explain it from the formula I posted above?

bump...

bump...two days and no answer at all?

Homework Statement We the domain be the unit disc D: D=\left \{(x,y):x^{2}+y^{2}<1 \right \} let u(x,y) solve: -\triangle u+(u_{x}+2u_{y})u^{4}=0 on D boundary: u=0 on \partial D One solution is u=0. Is it the only solution?Homework Equations Divergence Theorem "Energy Method"The Attempt at...

Say you have an arbitrary function f(x,y) and you have the partial derivative fx How would you go about finding the general form of this integral? \int f^{5}(f_{x}+2f_{y}) I wanted to treat fx+fy = df, but the constant 2 really messes that up.

Well, I meant f(x,y) to just be an arbitrary function of x and y. My question was meant to find out what the general form of the integral would be. Sorry for the confusion!

Maybe I am not being clear. What I just want to know is how this solution shows that it extends outwards at t>0 and why it continues to exist at all later times. In other words, can somebody prove to me why Hyugen's principle fails at dimension 2?

Hello, I have some trouble seeing why the solution of the wave equation in 2 dimensions exist at all later times once it passes an initial disturbance... For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain...

Oh, nevermind, I got it =]

bump...I have kind of a part two question depending on how correct my answer is.

bump, am I being too confusing here?

Hello, maybe in a traditional pde view, it would be more helpful to think of y as t for time?

Homework Statement Assume we are in the open first quadrant in the (x,y) plane Say we have u(x,y) a C1 function in the closed first quadrant that satisfies the PDE: u_{y}=3u_{x} in the open first quadrant Boundary Conditions: u(0,y)=0 for t greater than or equal to 0 u(x,0)= g(x) for x...

Ah ok. Thanks

Hello, I came upon this strange integral: \int \frac{f(x,y)}{x}dx How would one attempt to solve this? Would integration by parts do?