How to plot two time intervals of a graph simultaneously?

Question

The graphs of my provided code look approximately like the one in the picture below. How is it possible to plot such graphs? Please help how to break the axis scale as shown. Any suggestion appreciated. Thanks a lot.

Subscript[C, i]=2.5*10^6
Subscript[k, e]=315
σ=1*10^-9
Subscript[S, e]=1.58*10^-5
g=2.3*10^16
Subscript[C, e]=2.1*10^4
τ=1*10^-15
a=1/τ
Subscript[w, 1]=1
Subscript[s, 1]=y/(Subscript[w, 1]*σ)
Subscript[b, 1]=g/Subscript[C, e]*(1+(Subscript[k, e]*Subscript[s, 1]^2)/g)
Subscript[Δ, 1]=Sqrt[Subscript[b, 1]^2-4*Subscript[k, e]*Subscript[s, 1]^2*g/(Subscript[C, i]*Subscript[C, e])]
Subscript[p, 11]=(-Subscript[b, 1]+Subscript[Δ, 1])/2
Subscript[p, 12]=(-Subscript[b, 1]-Subscript[Δ, 1])/2
Subscript[T, i]=(Subscript[S, e]*g)/(2*π*τ*Subscript[C, i]*Subscript[C, e])*NIntegrate[BesselJ[0,y]*Exp[-((σ^2*Subscript[s, 1]^2)/4)]*(Exp[-a*t]/((a+Subscript[p, 11])*(a+Subscript[p, 12]))+1/(Subscript[p, 11]-Subscript[p, 12])*(Exp[Subscript[p, 11]*t]/(Subscript[p, 11]+a)-Exp[Subscript[p, 12]*t]/(Subscript[p, 12]+a)))*y/(σ*Subscript[w, 1])^2,{y,0,100}]
Subscript[T, e]=Subscript[T, i]+Subscript[S, e]/(2*π*τ*Subscript[C, e])*NIntegrate[BesselJ[0,y]*Exp[-((σ^2*Subscript[s, 1]^2)/4)]*(-((a*Exp[-a*t])/((a+Subscript[p, 11])*(a+Subscript[p, 12])))+1/(Subscript[p, 11]-Subscript[p, 12])*((Subscript[p, 11]*Exp[Subscript[p, 11]*t])/(Subscript[p, 11]+a)-(Subscript[p, 12]*Exp[Subscript[p, 12]*t])/(Subscript[p, 12]+a)))*y/(σ*Subscript[w, 1])^2,{y,0,100}]
Plot[Subscript[T, e],{t,0,1*10^-14}]
Plot[Subscript[T, i],{t,0,1*10^-14}]

Answer 1

First, I recommend that you avoid using subscripts except for display.

Since the range of your plots is only {t, 0, 10^-14} there are no regions where the functions are essentially constant and where a gap in the axis would be appropriate.

Clear["Global`*"]

Format[Ti] = Subscript[T, i];
Format[Te] = Subscript[T, e];

Ci = 25*10^5;
ke = 315;
σ = 1*10^-9;
Se = 158*10^-7;
g = 23*10^15;
Ce = 21*10^3;
τ = 1*10^-15;
a = 1/τ;
s1[w_] = y/(w*σ);
b1[w_] = g/Ce*(1 + (ke*s1[w]^2)/g);
Δ1[w_] = Sqrt[b1[w]^2 - 4*ke*s1[w]^2*g/(Ci*Ce)];
p11[w_] = (-b1[w] + Δ1[w])/2;
p12[w_] = (-b1[w] - Δ1[w])/2;

wValues = {1, 3, 5};

Ti[t_?NumericQ, w_?NumericQ] :=
 (Se*g)/(2*π*τ*Ci*Ce)*
  NIntegrate[BesselJ[0, y]*Exp[-((σ^2*s1[w]^2)/4)]*
    (Exp[-a*t]/((a + p11[w])*(a + p12[w])) +
      1/(p11[w] - p12[w])*
       (Exp[p11[w]*t]/(p11[w] + a) -
         Exp[p12[w]*t]/(p12[w] + a)))*y/(σ*w)^2,
   {y, 0, 100},
   WorkingPrecision -> 15]

Te[t_?NumericQ, w_?NumericQ] := 
 Ti[t, w] + Se/(2*π*τ*Ce)*
   NIntegrate[BesselJ[0, y]*Exp[-((σ^2*s1[w]^2)/4)]*
     (-((a*Exp[-a*t])/((a + p11[w])*(a + p12[w]))) + 
       1/(p11[w] - p12[w])*
        ((p11[w]*Exp[p11[w]*t])/(p11[w] + a) - 
          (p12[w]*Exp[p12[w]*t])/(p12[w] + a)))*
     y/(σ*w)^2, 
    {y, 0, 100},
    WorkingPrecision -> 15]

Legended[
  Column[
   Plot[
      Evaluate@Table[#[t, w], {w, wValues}], 
      {t, 0, 10^-14},
      PlotRange -> All,
      Frame -> True,
      FrameLabel -> {None,
        Style[StringForm["``[t]", #], 12, Bold]},
      WorkingPrecision -> 15,
      PlotStyle -> {{Red, Dashed}, {Blue, Dotted}, Black},
      ImageSize -> Medium,
      ImagePadding -> {{60, 15}, {20, 8}},
      AspectRatio ->
       If[# === Te, 1/GoldenRatio, 1/3]] & /@ {Te, Ti}],
  Placed[
   LineLegend[
    {{Red, Dashed}, {Blue, Dotted}, Black},
    StringForm["w = ``", #] & /@ wValues],
   {.6, .9}]] // Quiet

Answer 2

Use the functions Te and Ti from Bob Hanlon's answer to get two plots for each function with desired plot ranges:

{xrangea, xrangeb} = {{0, 10^-14}, {10^-13, 10^-12}};

{yrange1, yrange2} = {{0, 8 10^6}, {0, 350}};

{plot1a, plot1b, plot2a, plot2b} = Quiet@Plot[
      Evaluate @ Table[#[t, w], {w, wValues}], {t, #2[[1]], #2[[2]]}, 
      PlotRange -> {All, #3}, 
      PlotRangePadding -> {Automatic, Scaled[.05]}, Axes -> False, 
      Frame -> True,
      FrameTicks -> {{Automatic, Automatic},
        {Charting`ScaledTicks[{Identity, Identity}][#, #2, 3] &, Automatic}}, 
      FrameLabel -> {None, #4}, WorkingPrecision -> 15, 
      PlotStyle -> {{Red, Dashed}, {Blue, Dotted}, Black},
      PlotLegends -> ({#, #4} /. {{_, None} | {Ti, _} -> None, {Te, _} -> 
        Placed[PromptForm[w , #] & /@ wValues, {.7, .8}]})] & @@@ 
   (Tuples[{{Te, Ti}, Thread[{{xrangea, xrangeb}, {lbl, None}}]}] /. 
    {a_, {b_, c_}} :> {a, b, a /. {Te -> yrange1, Ti -> yrange2}, 
      c /. lbl -> Style[a[t], 12, Bold]});

and combine the four plots using Lukas Lang's ResourceFunction["PlotGrid"]

ResourceFunction["PlotGrid"][{{plot1a, plot1b}, {plot2a, plot2b}}, 
 "MergeAxes" -> {"Cut", False}, Spacings -> {20, 30}, 
 ImageSize -> 700, AspectRatio -> 1/GoldenRatio, 
 ItemSize -> {{{Scaled}, Scaled[.005]}, {700, 300}}]