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Math Help - Well-posed Schrödinger equation

  1. #1
    Junior Member
    Joined
    Dec 2005
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    34

    Well-posed Schrödinger equation

    hi,
    i need to find non trivial conditions, for which the following system is well posed.
    and then prove it is well posed.

    <br />
u_{t}=\imath [A_{1}u_{xx} + A_{2}u_{yy}] \ + \ B_{1}u_{x}+B_{2}u_{y} \ +\ Cu \ +\ F   \   <br />
         <br />
u(t=0,x)=f(x);\    f(x)=f(x+2\pi)     \  <br />
    <br />
u\in C^N; \    A_j,B_j,C_j\in C^N; \    A_j=A_j^*; \    j=1,2<br />
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  2. #2
    Junior Member
    Joined
    Dec 2005
    Posts
    34
    the conditions should be on B obiuosly.
    but i dont know of what kind, and how to prove it is well posed

    i dont must use the optimal B, but i need one that would be easy to prove
    i guess that taking B to be unitare ( B=B*), will solve it, but i'm not sure
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