# 瞬态诺伊曼值

 In[1]:= X\[CapitalOmega] = ImplicitRegion[ y >= 0 && (x - 3/2)^2 + y^2 >= 1/25 && x^2 + y^2 >= 1 && x^2 + y^2 <= 4 && y <= x Tan[\[Pi]/8], {x, y}];

 In[2]:= XSubscript[\[CapitalGamma], N][t_] = NeumannValue[ If[t <= 10., -100. t, -1000.], (x - 3/2)^2 + y^2 == 1/25];
 In[3]:= XSubscript[\[CapitalGamma], D][ t_] = {DirichletCondition[u[t, x, y] == 200., x^2 + y^2 == 1], DirichletCondition[u[t, x, y] == 15., x^2 + y^2 == 4]};

 In[4]:= Xuinit = NDSolveValue[{10 \!\( \*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(u[0, x, y]\)\) == 0, Subscript[\[CapitalGamma], D][0]}, u[0, x, y], {x, y} \[Element] \[CapitalOmega], Method -> {"PDEDiscretization" -> {"FiniteElement", "MeshOptions" -> {"BoundaryMeshGenerator" -> "Continuation"}}}];

 In[5]:= Xuif = NDSolveValue[{D[u[t, x, y], t] - 10 \!\( \*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(u[t, x, y]\)\) == Subscript[\[CapitalGamma], N][t], Subscript[\[CapitalGamma], D][0], u[0, x, y] == uinit}, u, {t, 0, 25}, {x, y} \[Element] Head[uinit]["ElementMesh"]];

Out[7]=
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