PDE terminal condition problem












1












$begingroup$


I have this terminal value problem:



$aU = (1-t)U_t + bU_{xx}$, with a, and b constants, $t in [0,1]$, and $x in mathbb{R}$



s.t.



U(x,1) = g(x)



In my attempt to solve it I applied a Fourier transform since I know that $ lim_{|x|rightarrow infty} U(x,t) = 0$, however, the fact that $(1-t)$ goes to $0$ as $t rightarrow 1$ made me get lost. Does anyone know how to overcome this?










share|cite|improve this question











$endgroup$

















    1












    $begingroup$


    I have this terminal value problem:



    $aU = (1-t)U_t + bU_{xx}$, with a, and b constants, $t in [0,1]$, and $x in mathbb{R}$



    s.t.



    U(x,1) = g(x)



    In my attempt to solve it I applied a Fourier transform since I know that $ lim_{|x|rightarrow infty} U(x,t) = 0$, however, the fact that $(1-t)$ goes to $0$ as $t rightarrow 1$ made me get lost. Does anyone know how to overcome this?










    share|cite|improve this question











    $endgroup$















      1












      1








      1


      2



      $begingroup$


      I have this terminal value problem:



      $aU = (1-t)U_t + bU_{xx}$, with a, and b constants, $t in [0,1]$, and $x in mathbb{R}$



      s.t.



      U(x,1) = g(x)



      In my attempt to solve it I applied a Fourier transform since I know that $ lim_{|x|rightarrow infty} U(x,t) = 0$, however, the fact that $(1-t)$ goes to $0$ as $t rightarrow 1$ made me get lost. Does anyone know how to overcome this?










      share|cite|improve this question











      $endgroup$




      I have this terminal value problem:



      $aU = (1-t)U_t + bU_{xx}$, with a, and b constants, $t in [0,1]$, and $x in mathbb{R}$



      s.t.



      U(x,1) = g(x)



      In my attempt to solve it I applied a Fourier transform since I know that $ lim_{|x|rightarrow infty} U(x,t) = 0$, however, the fact that $(1-t)$ goes to $0$ as $t rightarrow 1$ made me get lost. Does anyone know how to overcome this?







      pde fourier-transform






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      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 10 at 22:50







      Nicolas Pimentel de Souza

















      asked Jan 10 at 18:05









      Nicolas Pimentel de SouzaNicolas Pimentel de Souza

      134




      134






















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