自己整了个细胞建模，其中有一个必要公式u5（x，t）对x从1到0定积分=u6（t）对t的偏导数，u7(t)＝u6（t）+1，而u7（t）又与u1（x，t）联立。所有方程均未知，只知道关系式。
源代码太长放在楼下了，问了几个学过mathematica的朋友都说未知方程不能将定积分包含在式子里面，请大佬们帮忙指点一下怎么改合适，小弟给各位磕头了

sol61115 = NDSolve[{D[u1[x, t], t] == 1*D[u1[x, t], {x, 2}] + 0.1 - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) + 1*1*(1 + Exp[((1*1^2/(1^2 + 1^2) + 1 - u7[t]))/1]) + 1*1*1*u1[x, t]^2*u2[x, t]^2* u3[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)) + 1*1*1*u1[x, t]^2*u2[x, t]^2* u4[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)),(*胞内钙离子浓度*) D[u2[x, t], t] == 1*D[u2[x, t], {x, 2}] - (1*1/(1 + 1))*u1[x, t]/(u1[x, t] + 1) - 1*u2[x, t],(*钙库离子浓度*) 1*D[u3[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u3[x, t],(*钙库一通道开放分数之一*) 1*D[u4[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u4[x, t],(*钙库二通道开放分数之一*) D[u5[x, t], t] == 1*D[u5[x, t], {x, 2}] - 1*(3 - u5[x, t])*u5[x, t]^2/(u5[x, t]^2 + 1^2) + 1/(1 + Exp[(2 - 1)/1]) - (1/((1 + (1 + 1)^4)/(1 + 1*1)^4*1* Exp[1*u7[t]/(1 + 1)])),(*胞内钾离子浓度*) D[u6[t], t] == integrate[ u5[x, t], {x, 0, 1}],(*电位差变化*) u7[t] == 1 + u6[t],(*细胞膜电位差*) u1[x, 0] == 1, u2[x, 0] == 1, u3[x, 0] == 0.2, u4[x, 0] == 0.2, u5[x, 0] == 1, u6[0] == 1, u7[0] == 2, Derivative[1, 0][u1][0, t] == 0, Derivative[1, 0][u1][1, t] == 0, Derivative[1, 0][u2][0, t] == 0, Derivative[1, 0][u2][1, t] == 0, Derivative[1, 0][u5][0, t] == 0, Derivative[1, 0][u5][1, t] == 0}, (*边界条件*){u1, u2, u3, u4, u5, u6, u7}, {x, 0, 1}, {t, 0, 1}]Clear@DerivativePlot3DPlot3D[Evaluate[{u1[x, t], u2[x, t], u7[t]} /. sol61115], {t, 0, 1}, {x, 0, 1}, PlotRange -> All, AxesLabel -> {x, t, u}, PlotStyle -> {{Opacity[.3], Blue}, {Opacity[.3], Red}, {Opacity[.3], Green}}, MeshFunctions -> {#3 &}]

其实也就改了u5到u7的内容，其他地方没有动，在不定积分改成定积分之前是可以运行的

这个是还没改完的不定积分代码，可以跑的
sol61115 = NDSolve[{D[u1[x, t], t] == 1*D[u1[x, t], {x, 2}] + 0.1 - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) + 1*1*(1 + Exp[((1*1^2/(1^2 + 1^2) + 1 - u7[x, t]))/1]) + 1*1*1*u1[x, t]^2*u2[x, t]^2* u3[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)) + 1*1*1*u1[x, t]^2*u2[x, t]^2* u4[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)),(*胞内钙离子浓度*) D[u2[x, t], t] == 1*D[u2[x, t], {x, 2}] - (1*1/(1 + 1))*u1[x, t]/(u1[x, t] + 1) - 1*u2[x, t],(*钙库离子浓度*) 1*D[u3[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u3[x, t],(*钙库一通道开放分数之一*) 1*D[u4[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u4[x, t],(*钙库二通道开放分数之一*) D[u5[x, t], t] == 1*D[u5[x, t], {x, 2}] - 1*(3 - u5[x, t])*u5[x, t]^2/(u5[x, t]^2 + 1^2) + 1/(1 + Exp[(2 - 1)/1]) - (1/((1 + (1 + 1)^4)/(1 + 1*1)^4*1* Exp[1*u7[x, t]/(1 + 1)])),(*胞内钾离子浓度*) D[u6[x, t], t, x] == u5[x, t],(*电位差变化*) u7[x, t] == 1 + u6[x, t],(*细胞膜电位差*) u1[x, 0] == 1, u2[x, 0] == 1, u3[x, 0] == 0.2, u4[x, 0] == 0.2, u5[x, 0] == 1, u6[x, 0] == 1, u7[x, 0] == 2, Derivative[1, 0][u1][0, t] == 0, Derivative[1, 0][u1][1, t] == 0, Derivative[1, 0][u2][0, t] == 0, Derivative[1, 0][u2][1, t] == 0, Derivative[1, 0][u5][0, t] == 0, Derivative[1, 0][u5][1, t] == 0}, (*边界条件*){u1, u2, u3, u4, u5, u6, u7}, {x, 0, 1}, {t, 0, 1}]Clear@DerivativePlot3DPlot3D[Evaluate[{u1[x, t], u2[x, t], u7[x, t]} /. sol61115], {t, 0, 1}, {x, 0, 1}, PlotRange -> All, AxesLabel -> {x, t, u}, PlotStyle -> {{Opacity[.3], Blue}, {Opacity[.3], Red}, {Opacity[.3], Green}}, MeshFunctions -> {#3 &}]

改了一个比较简单的格式，但还是不行。。
sol61115 = NDSolve[{D[u1[x, t], t] == 1*D[u1[x, t], {x, 2}] + 0.1 - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) + 1*1*(1 + Exp[((1*1^2/(1^2 + 1^2) + 1 - u7[1, t]))/1]) + 1*1*1*u1[x, t]^2*u2[x, t]^2* u3[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)) + 1*1*1*u1[x, t]^2*u2[x, t]^2* u4[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)),(*胞内钙离子浓度*) D[u2[x, t], t] == 1*D[u2[x, t], {x, 2}] - (1*1/(1 + 1))*u1[x, t]/(u1[x, t] + 1) - 1*u2[x, t],(*钙库离子浓度*) 1*D[u3[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u3[x, t],(*钙库一通道开放分数之一*) 1*D[u4[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u4[x, t],(*钙库二通道开放分数之一*) D[u5[x, t], t] == 1*D[u5[x, t], {x, 2}] - 1*(3 - u5[x, t])*u5[x, t]^2/(u5[x, t]^2 + 1^2) + 1/(1 + Exp[(2 - 1)/1]) - (1/((1 + (1 + 1)^4)/(1 + 1*1)^4*1* Exp[1*u7[1, t]/(1 + 1)])),(*胞内钾离子浓度*) D[u6[x, t], t, x] == u5[x, t],(*电位差变化*) u7[x, t] == 1 + u6[x, t],(*细胞膜电位差*) u1[x, 0] == 1, u2[x, 0] == 1, u3[x, 0] == 0.2, u4[x, 0] == 0.2, u5[x, 0] == 1, u6[x, 0] == 1, u7[x, 0] == 2, Derivative[1, 0][u1][0, t] == 0, Derivative[1, 0][u1][1, t] == 0, Derivative[1, 0][u2][0, t] == 0, Derivative[1, 0][u2][1, t] == 0, Derivative[1, 0][u5][0, t] == 0, Derivative[1, 0][u5][1, t] == 0}, (*边界条件*){u1, u2, u3, u4, u5, u6, u7}, {x, 0, 1}, {t, 0, 1}]Clear@DerivativePlot3DPlot3D[Evaluate[{u1[x, t], u2[x, t], u7[1, t]} /. sol61115], {t, 0, 1}, {x, 0, 1}, PlotRange -> All, AxesLabel -> {x, t, u}, PlotStyle -> {{Opacity[.3], Blue}, {Opacity[.3], Red}, {Opacity[.3], Green}}, MeshFunctions -> {#3 &}]

解开了此贴终结，代码太长了可以私我