Hello.
I have 2D Euler equation for fluids. I can't derive it in polar coordinates. I defined functions u(x,y,t) = u'(r, theta, t) and v(x,y,t) = v'(r, theta, t). I started by computing derivatives
\frac{\partial u'}{\partial r}=\cos\theta\frac{\partial u}{\partial...
I need to find two functions I_1, I_2 constant on charakterstics and write general solution
u(x,y,t)=\varphi(I_1,I_2)
I found one function
I_1=x_1^2+x_2^2
I don't know to find second one with t. Thx
Hello,
I have a problem in the form
\frac{\partial u}{\partial t}+\frac{\partial u}{\partial x}+e^{x}u=0
with conditions
u(x,0)=u_0(x)
u(0,t)=\int_{0}^{\infty}f(x)u(x,t)dx
Im confused, because in first order PDE i require only 1 condition. How to solve this for two conditions?
Thank you ! Navier-Stokes without pressure? It is strange, because in order to get particles move, we have to include pressure considerations. How would you interpretate that ?
Hello, I have Navier stokes in 1D
\rho\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}\right)=-\frac{\partial p}{\partial x}+\mu\frac{\partial^2u}{\partial x^2}
Condition of imcompressibility gives
\frac{\partial u}{\partial x}=0
So I have Navier stokes...
Hello,
I derived a model in the form
\begin{array}{rcl}\frac{\partial U(\vec{x},t)}{\partial t}&=&\gamma^2\Vert\nabla U(\vec{x},t)\Vert,\\\int_{\Omega}U(\vec{x},t)\, d \Omega&=&U_0,\quad\forall t\\U(\vec{x},0)&=&f(\vec{x}).\end{array}
I don't know to solve that.
THanks for help.
Thanks for help so much to all. But any of these replies didn't satisfied me, but now I
solved my problem.
To yuiop: The problem is, what the hell is L\sqrt{1-v^2/c^2} :-) Of course, I
know what is it, but we didn't derive it here.
To PAllen: This was that obstacle :-) I really...
Hello !
Can you tell me what's wrong? I suppose two observers. They measure speed of light. One observer is in rocket of length L. Observer in rocket measured speed
C'=\frac{L}{t'}
and t' is time from observer's view. Second observer is outside. He measured
C=\frac{L+vt}{t}
where v is...
We want to prove
\forall \varepsilon>0\quad\exists\delta>0\quad\forall (x,y)\in B_{\delta}(x_0,y_0):f(x,y)\in B_{\varepsilon}(f(x_0,y_0))
Let fix epsilon and we want to find such delta. From definition of ball B, we compute...
Hello!
I recently tried to prove following theorem: Let \phi:B\to\mathbb{R}^2 be a diffeomorphism (regular, injective mapping). Then
\int_{\phi(B)}f(\mathbf{x})\,\mathrm{d}x=\int_{B}f(\phi(\mathbf{t}))\left|{\mathrm{det}}\mathbf{J}_{\phi}\right|\mathrm{d}t
With following I can't proof...
Hello !
When I'm reading something about differential equations everywhere it's about open sets. For example when we define special kind of equation
x'=f(t,x)\,;\;f:\Omega\subset\mathbb{R}\times\mathbb{R}\to\mathbb{R}
Omega is open. Why Omega must be open? Thanks
Hello,
I nowhere find general form of energy conservation law, but in one book i found this
(*)\hspace{1cm}E=E_{in}-E_{out}+E_{generated}
where E(in) is energy flow into system, E(out) is energy flow out of system and E(generated) is energy generated. It was in sense of heat...