How to solve this Cauchy problem

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I am struggeling with the following PDE:



$u_t+a(x,y)u_xx+b(x,y)u_xy+c(x,y)u_yy+d(x,y)u_x+e(x,y)u_y+f(x,y)u=0$
$u(T,x,y)=1,$



where $a,b,c,d,e,f$ are polynomials and the domain is the set $(t,x,y):tin[0,T],x+y=1,xgeq0,ygeq0$.



I showed, however, that there exists a unique solution and I would like to have this solution explicitly, either via Maple/Matlab or by hand. My problem hereby is that this PDE is not in the right form for Matlab, Maple is not able to solve it (here my post in mapleprime) and I don't know how to handle this by hand.



Thanks a lot for your help.



Best regards,



utcyp




pde numerical-methods matlab maple linear-pde




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    I am struggeling with the following PDE:



    $u_t+a(x,y)u_xx+b(x,y)u_xy+c(x,y)u_yy+d(x,y)u_x+e(x,y)u_y+f(x,y)u=0$
    $u(T,x,y)=1,$



    where $a,b,c,d,e,f$ are polynomials and the domain is the set $(t,x,y):tin[0,T],x+y=1,xgeq0,ygeq0$.



    I showed, however, that there exists a unique solution and I would like to have this solution explicitly, either via Maple/Matlab or by hand. My problem hereby is that this PDE is not in the right form for Matlab, Maple is not able to solve it (here my post in mapleprime) and I don't know how to handle this by hand.



    Thanks a lot for your help.



    Best regards,



    utcyp




    pde numerical-methods matlab maple linear-pde




    share|cite|improve this question























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I am struggeling with the following PDE:



      $u_t+a(x,y)u_xx+b(x,y)u_xy+c(x,y)u_yy+d(x,y)u_x+e(x,y)u_y+f(x,y)u=0$
      $u(T,x,y)=1,$



      where $a,b,c,d,e,f$ are polynomials and the domain is the set $(t,x,y):tin[0,T],x+y=1,xgeq0,ygeq0$.



      I showed, however, that there exists a unique solution and I would like to have this solution explicitly, either via Maple/Matlab or by hand. My problem hereby is that this PDE is not in the right form for Matlab, Maple is not able to solve it (here my post in mapleprime) and I don't know how to handle this by hand.



      Thanks a lot for your help.



      Best regards,



      utcyp




      pde numerical-methods matlab maple linear-pde




      share|cite|improve this question













      I am struggeling with the following PDE:



      $u_t+a(x,y)u_xx+b(x,y)u_xy+c(x,y)u_yy+d(x,y)u_x+e(x,y)u_y+f(x,y)u=0$
      $u(T,x,y)=1,$



      where $a,b,c,d,e,f$ are polynomials and the domain is the set $(t,x,y):tin[0,T],x+y=1,xgeq0,ygeq0$.



      I showed, however, that there exists a unique solution and I would like to have this solution explicitly, either via Maple/Matlab or by hand. My problem hereby is that this PDE is not in the right form for Matlab, Maple is not able to solve it (here my post in mapleprime) and I don't know how to handle this by hand.



      Thanks a lot for your help.



      Best regards,



      utcyp





      pde numerical-methods matlab maple linear-pde





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      share|cite|improve this question




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      asked 2 days ago









      utcyp

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