I am attempting to solve the equation below, which requires v[y,0]==0 for all y greater than 0. I have followed the /; approach to enforce this definition, as outlined in the DSolve/Delay Differential Equations page in the language documentation.


Wolfram simply outputs the cell back without an error message. I believe that my inequality restriction on y in the second boundary condition is the issue, but I am not sure how to proceed.

  • $\begingroup$ I want to solve on {y, 0, Infinity}. The problem is startup of Couette flow. $\endgroup$
    – eoncarlyle
    Commented Feb 21, 2019 at 16:29
  • $\begingroup$ Do you want an analytical solution or a numerical one? $\endgroup$ Commented Feb 21, 2019 at 16:31
  • $\begingroup$ I want an analytical solution, which I am confident exists $\endgroup$
    – eoncarlyle
    Commented Feb 21, 2019 at 16:34
  • $\begingroup$ The solution exists on the half-line. See answer. $\endgroup$ Commented Feb 21, 2019 at 17:13

1 Answer 1



sol= DSolve[{Derivative[2, 0][v][y, t] == Derivative[0, 1][v][y, t], 
       v[0, t] == 1, v[y, 0] == 0}, v, {y, 0, Infinity}, {t, 0, Infinity}]
    Plot3D[Evaluate[v[y, t] /. First[sol]], {y, 0, 5}, {t, 0, 10}, 
     PlotRange -> All]



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