Heat Equation Analysis

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I have a question and I'm not really sure how to get the initial condition from the question. I've managed to determine $U(x,t)$ from $u(x,t) = U(x,t) + psi(x)$ by modifying the boundary condition to = 0 but I still can't seem to determine the initial condition, which is why I am stuck after $U(x,t)$.



I don't need the exact question but a hint towards finding that initial condition.



Any help would be greatly appreciated!



This is the question



I understand that the BC are $u(0,t) = 120$ and $u(20,t) = 30$ and the rest is just normal working but the initial condition is bugging me.



Thank you!




pde boundary-value-problem heat-equation




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    up vote
    0
    down vote

    favorite












    I have a question and I'm not really sure how to get the initial condition from the question. I've managed to determine $U(x,t)$ from $u(x,t) = U(x,t) + psi(x)$ by modifying the boundary condition to = 0 but I still can't seem to determine the initial condition, which is why I am stuck after $U(x,t)$.



    I don't need the exact question but a hint towards finding that initial condition.



    Any help would be greatly appreciated!



    This is the question



    I understand that the BC are $u(0,t) = 120$ and $u(20,t) = 30$ and the rest is just normal working but the initial condition is bugging me.



    Thank you!




    pde boundary-value-problem heat-equation




    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I have a question and I'm not really sure how to get the initial condition from the question. I've managed to determine $U(x,t)$ from $u(x,t) = U(x,t) + psi(x)$ by modifying the boundary condition to = 0 but I still can't seem to determine the initial condition, which is why I am stuck after $U(x,t)$.



      I don't need the exact question but a hint towards finding that initial condition.



      Any help would be greatly appreciated!



      This is the question



      I understand that the BC are $u(0,t) = 120$ and $u(20,t) = 30$ and the rest is just normal working but the initial condition is bugging me.



      Thank you!




      pde boundary-value-problem heat-equation




      share|cite|improve this question














      I have a question and I'm not really sure how to get the initial condition from the question. I've managed to determine $U(x,t)$ from $u(x,t) = U(x,t) + psi(x)$ by modifying the boundary condition to = 0 but I still can't seem to determine the initial condition, which is why I am stuck after $U(x,t)$.



      I don't need the exact question but a hint towards finding that initial condition.



      Any help would be greatly appreciated!



      This is the question



      I understand that the BC are $u(0,t) = 120$ and $u(20,t) = 30$ and the rest is just normal working but the initial condition is bugging me.



      Thank you!





      pde boundary-value-problem heat-equation





      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 22 at 7:38









      Harry49

      4,8702825




      4,8702825










      asked Dec 9 '17 at 22:48









      Eugene Zhang

      12




      12




















          1 Answer
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          There is a misunderstanding of the problem. Let us draw the initial configuration:



          config



          Mathematically, this could be written as an initial- and boundary-value problem for the heat equation $partial_t u = Dpartial_xx u$. The initial conditions are
          $$
          u(x,0) = leftlbrace
          beginaligned
          &120 & & textif; 0leq xleq 15, ,\
          &30 & & textif; 15leq xleq 20, ,
          endalignedright .
          $$
          The boundary conditions are $u(0,t)=u(20,t)=30$ for $t>0$.






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            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

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            active

            oldest

            votes








            up vote
            0
            down vote













            There is a misunderstanding of the problem. Let us draw the initial configuration:



            config



            Mathematically, this could be written as an initial- and boundary-value problem for the heat equation $partial_t u = Dpartial_xx u$. The initial conditions are
            $$
            u(x,0) = leftlbrace
            beginaligned
            &120 & & textif; 0leq xleq 15, ,\
            &30 & & textif; 15leq xleq 20, ,
            endalignedright .
            $$
            The boundary conditions are $u(0,t)=u(20,t)=30$ for $t>0$.






            share|cite|improve this answer
























              up vote
              0
              down vote













              There is a misunderstanding of the problem. Let us draw the initial configuration:



              config



              Mathematically, this could be written as an initial- and boundary-value problem for the heat equation $partial_t u = Dpartial_xx u$. The initial conditions are
              $$
              u(x,0) = leftlbrace
              beginaligned
              &120 & & textif; 0leq xleq 15, ,\
              &30 & & textif; 15leq xleq 20, ,
              endalignedright .
              $$
              The boundary conditions are $u(0,t)=u(20,t)=30$ for $t>0$.






              share|cite|improve this answer






















                up vote
                0
                down vote










                up vote
                0
                down vote









                There is a misunderstanding of the problem. Let us draw the initial configuration:



                config



                Mathematically, this could be written as an initial- and boundary-value problem for the heat equation $partial_t u = Dpartial_xx u$. The initial conditions are
                $$
                u(x,0) = leftlbrace
                beginaligned
                &120 & & textif; 0leq xleq 15, ,\
                &30 & & textif; 15leq xleq 20, ,
                endalignedright .
                $$
                The boundary conditions are $u(0,t)=u(20,t)=30$ for $t>0$.






                share|cite|improve this answer












                There is a misunderstanding of the problem. Let us draw the initial configuration:



                config



                Mathematically, this could be written as an initial- and boundary-value problem for the heat equation $partial_t u = Dpartial_xx u$. The initial conditions are
                $$
                u(x,0) = leftlbrace
                beginaligned
                &120 & & textif; 0leq xleq 15, ,\
                &30 & & textif; 15leq xleq 20, ,
                endalignedright .
                $$
                The boundary conditions are $u(0,t)=u(20,t)=30$ for $t>0$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Aug 22 at 8:38









                Harry49

                4,8702825




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