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Nonlinear Partial Differential Equation paid collaboration needed

Tao Guo Tao Guo, Shanghai Institute of Materia Medica, CAS Posted 1 year ago .root-post .like-component { align-items: center; } .root-post .like-button { margin-left: 0; }

I will pay $200 for the solution of the following nonlinear Partial Differential Equation using Wolfram Technologies:
email:gotallcn@gmail.com

POSTED BY: Tao Guo

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Tao Guo Tao Guo, Shanghai Institute of Materia Medica, CAS Posted 1 year ago

POSTED BY: Tao Guo

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Mariusz Iwaniuk Mariusz Iwaniuk, engineer, math hobbyist. Posted 1 year ago

I'm not a expert for solving this kind equation, but using FiniteElement method with coefficient = 3/2, I have:

     usol2 = Block[{\[Epsilon] = $MachineEpsilon, inf = 48, 
         coeff = 1 + 1/2}, 
        NDSolveValue[{I*
            D[M[r, t], 
             t] == (-E^-M[r, t])*(D[M[r, t], r, r] - (D[M[r, t], r])^2 + (
               2 D[M[r, t], r])/r) - 
            NeumannValue[M[r, t], r == \[Epsilon]], 
          DirichletCondition[M[r, t] == coeff*E^(-(r^2/2)), t == 0], 
          DirichletCondition[M[r, t] == 0, r == inf]}, 
         M, {r, \[Epsilon], inf}, {t, 0, 2}, 
         Method -> {"FiniteElement", "InterpolationOrder" -> {M -> 2}, 
           "MeshOptions" -> {"MaxCellMeasure" -> 2/100}}]];
     xv = NArgMax[Norm[usol2[0, t]], {t, 1/10, 5/10}];
     Show[Plot3D[2 Norm[usol2[r, t]], {r, 0, 3}, {t, 0, 2}, 
       PlotRange -> All, 
       AxesLabel -> {Style["r ", Italic], Style["t", Italic], 
         Rotate["\[LeftBracketingBar]M(r, t)\[RightBracketingBar]", \[Pi]/
          2]}, ViewPoint -> {3, -2.2, 4.1}, MaxRecursion -> 4], 
      ParametricPlot3D[{r, xv, 2 Norm[usol2[r, xv]]}, {r, 0, 3}, 
       PlotStyle -> Directive[Red, Thickness -> 0.005]]]

enter image description here

Maybe you post question here ,you got a better answer.

Regards M.I.

POSTED BY: Mariusz Iwaniuk

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Tao Guo Tao Guo, Shanghai Institute of Materia Medica, CAS Posted 1 year ago

Hello Mariusz Iwaniuk,

Thank you for sharing your valuable information with me. I appreciate the time and effort you took to provide them.

Regards,
Tao Guo

POSTED BY: Tao Guo

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Sam Carrettie Sam Carrettie, Freelancer Posted 1 year ago

Hi @Tao, are you looking for numeric or exact symbolic solution? If numeric, would solutions for large enough (but not infinity) radius suffice as an approximation? If you have any other thoughts or background or references for this problem, it would be very helpful, as well as any initial setup in form of Wolfram Language code that you have may tried already.

POSTED BY: Sam Carrettie

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Tao Guo Tao Guo, Shanghai Institute of Materia Medica, CAS Posted 1 year ago

Hi @Sam, I apologize for the confusion! I realized that I responded to you in the wrong location.

POSTED BY: Tao Guo

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