I defined a function, but it takes a long time to show its result. It will also take long time to use this function later.
p1[x_, t_] := pinf + (A2 (-1 + E^(-t \[Theta]c)))/\[Theta]c + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(t\)]\(
\*FractionBox[\(A11\
\*SuperscriptBox[\(E\), \(\(-
\*FractionBox[
SuperscriptBox[\(A10\), \(2\)], \(t1\)]\) + A3\ \((\(-t1\) + t)\) -
t1*\ \[Theta]c\)]\),
SqrtBox[\(t1\)]] \[DifferentialD]t1\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(t\)]\(\((\(-A8\) + A9 -
A15\
\*SuperscriptBox[\(E\), \(A3\ \((\(-t1\) + t)\)\)] - A9\
\*SuperscriptBox[\(E\), \(\((t1 - t)\)\ \[Theta]c\)] - A16\
\*SuperscriptBox[\(E\), \(A3\ \((\(-t1\) + t)\)\)]\ Erf[
\*SqrtBox[\(A5\)]\
\*SqrtBox[\(\(-t1\) + t\)]])\)\ \((
\*FractionBox[
SuperscriptBox[\(E\), \(-
\*FractionBox[
SuperscriptBox[\(A12\), \(2\)], \(t1\)]\)], \(
\*SqrtBox[\(\[Pi]\)]\
\*SqrtBox[\(t1\)]\)] -
\*SqrtBox[\(Dp\)]\
\*SuperscriptBox[\(E\), \(\[Alpha]1\ \((2\ A12\
\*SqrtBox[\(Dp\)] + Dp\ t1*\ \[Alpha]1)\)\)]\ \[Alpha]1\ Erfc[
\*FractionBox[\(A12\
\*SqrtBox[\(Dp\)] + Dp\ t1*\ \[Alpha]1\),
SqrtBox[\(Dp\ t1\)]]])\) \[DifferentialD]t1\)\) /. {A10 -> (-lh + x)/(
2 Sqrt[Dc] ), A12 -> (-lh + x)/(2 Sqrt[Dp ])} // Simplify //
Normal
ep1 = p1[x, t][[1]]
ep2 = p1[x, t][[2]]
eq3 = p1[x, t][[3]]
eq5 = p1[x, t][[4]]