solve $u_t + x (u_x)^2 = f(x), x in (1,2) , t in (0,T)$ with $u(x,T) = g(x)$

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Assume $f,g$ smooth enough. Is there a chance that the problem below has a unique solution? How to proceed to the analysis of it?
$$
u_t + x (u_x)^2 = f(x), : (x,t) in (1,2) times (0,T)
$$
with $u(x,T) = g(x)$.
thanks.




pde




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    up vote
    1
    down vote

    favorite
    1












    Assume $f,g$ smooth enough. Is there a chance that the problem below has a unique solution? How to proceed to the analysis of it?
    $$
    u_t + x (u_x)^2 = f(x), : (x,t) in (1,2) times (0,T)
    $$
    with $u(x,T) = g(x)$.
    thanks.




    pde




    share|cite|improve this question
























      up vote
      1
      down vote

      favorite
      1









      up vote
      1
      down vote

      favorite
      1






      1





      Assume $f,g$ smooth enough. Is there a chance that the problem below has a unique solution? How to proceed to the analysis of it?
      $$
      u_t + x (u_x)^2 = f(x), : (x,t) in (1,2) times (0,T)
      $$
      with $u(x,T) = g(x)$.
      thanks.




      pde




      share|cite|improve this question














      Assume $f,g$ smooth enough. Is there a chance that the problem below has a unique solution? How to proceed to the analysis of it?
      $$
      u_t + x (u_x)^2 = f(x), : (x,t) in (1,2) times (0,T)
      $$
      with $u(x,T) = g(x)$.
      thanks.





      pde





      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 8 at 16:25









      zaphodxvii

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      asked Aug 8 at 16:16









      megaproba

      758




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