Results 1 to 3 of 3

Math Help - Heat equation with mixed boundary conditions

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    3

    Heat equation with mixed boundary conditions

    Does anyone know what is the solution of the heat equation
    u_t(x,t)=u_{xx}(x,t)

    with mixed boundary conditions
    u_x(0,t)=0
    u_x(1,t)=\epsilon u(1,t)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2010
    From
    Athens
    Posts
    45
    What exactly is ε?A simple constant?Do we know something about it?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    At x=0 there is no flow of temperature.
    At x=1 there is flow of temperature.

    But there must be initial conditions: the initial distribution of temperature
    u(x,0)=f(x) which changes in time due to flow of temperature (boundary conditions).
    You may try to solve by separation of variables
    u(x,t)=p(x)q(t).
    Last edited by zzzoak; October 27th 2010 at 03:01 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Heat Equation with Weird Boundary Conditions
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: September 29th 2011, 03:26 PM
  2. Help with Heat Equation with nonhomogeneous boundary conditions
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: November 14th 2010, 02:46 PM
  3. Heat Equation with Neumann Boundary conditions
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: September 24th 2010, 02:40 PM
  4. Replies: 0
    Last Post: April 26th 2010, 03:18 AM
  5. Boundary conditions in a heat equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: April 25th 2010, 12:07 PM

Search Tags


/mathhelpforum @mathhelpforum