Heat equation Definition and 257 Threads

\frac{\partial u}{\partial t} - k \frac{\partial^2 u}{\partial x^2} = 0 for 0 <x < pi, t> 0 u(0,t) = u(\pi,t) = 0 u(x,0) = x (\pi - x) OK i know the boring part of getting u(x,t) = X(x) T(t) the infinite series part is hard part the coefficient c_{n} = \frac{2}{\pi}...

Is there a straightforward proof for the existence of the one-dimensional linear heat equation f=u_t_-a^2*u_xx_=0. Is so, how? Note: _t_ represents the subscript, i.e., the derivative t, and _xx_ represents the subscript xx. Is the heat equation well posed? Can this proven? How?

Hi! Can someone please help? I'm trying to solve the heat equation in polar coordinates. Forgive my way of typing it in, I'm battling to make it look right. The d for derivative should be partial, alpha is the Greek alpha symbol and theta is the Greek theta symbol. du/dt =...

Hi, I'm not sure how to solve problems of this form: Uxx - Ut = h(x,t) where Uxx is second derivative of U(x,t) wrt x and Ut is first derivative of U(x,t) wrt t. Boundary conditions are as follows: U(0,t)=U(a,t)=U(x,0)=0 and h(x,t) is a fairly simple function, or even constant, say h=1...

What is the dimension of soln space of the heat equation: \frac{\partial U }{\partial t}=a^2\frac{\partial^2 U}{\partial x^2} U(0,t) = U(L,t) = 0 U(x,0)= f(x) Is it infinite , if so why?

Hello friends, does anybody have a soft copy of the following paper. if yes, then please mail it to my email address: aditya_tatu@yahoo.com aditya_tatu@da-iict.org I am not sure whether it is freely available online or not? the details of the paper are: Title : The heat equation...

I was wondering what happens if I want to solve the heat equation in a sphere surface, neglecting its thickness. I have one initial condition for T(t=0), in particular this initial profile can depend on azimuth and zenith angles, it is not uniform. Perhaps I have saying something stupid but I...