R = 0.045;L = 14;r = 0.009;e = 0.2;n = L/(\[Pi]*R*R);v = 4/3*Pi*r^3;g = (1 - 7/16*v)/(1 - v)^2; G = g*v;H = 1 + 1/(2*G);M = 1 + (9*\[Pi])/16*(1 + 2/(3*G))^2;k = 2/Sqrt[\[Pi]]*n*2*r*G*M*Sqrt[T[x, y]];\[CapitalGamma] = 4/Sqrt[\[Pi]]*(1 - e)*n*G*T[x, y]^1.5*1/(2*r);CirR = ImplicitRegion[x^2 + y^2 <= R^2, {x, y}];(*求解出n和T的分布，自变量为x和y，其中边界条件为：T在边界上沿径向偏导为0，n在区域内求积分等于L*)eqn1 = Simplify[{ Grad[T[x, y], {x, y}] == {GTx[x, y], GTy[x, y]}, (*Inactive[Div][k[x,y]*Inactive[Grad][T[x,y],{x,y}],{x,y}]*) k[x, y]*Div[{GTx[x, y], GTy[x, y]}, {x, y}] + Grad[k[x, y], {x, y}] . Grad[T[x, y], {x, y}] == \[CapitalGamma][x, y](*Integrate[ Integrate[n[x,y],{x,-Sqrt[R^2-y^2],Sqrt[R^2-y^2]}],{y,-R,R}]==L,*) , DirichletCondition[T[x, y] == 0.1, True]}];NDSolve[eqn1 , {T[x, y], GTx[x, y], GTy[x, y]}, {x, y} \[Element] CirR , Method -> {"PDEDiscretization" -> {"FiniteElement", "InitializePDECoefficientsOptions" -> {"VerificationData" -> \{"Coordinate" -> {0}}}}}]
