Btukfyl

How to adjust this expression

documentclass[a4paper,twoside,12pt]{ article}

usepackage[latin1,utf8,utf8x]{inputenc} 

usepackage[T1]{fontenc} 

usepackage[french]{babel} 

frenchbsetup{StandardLists=true}

usepackage{lmodern}

usepackage{amsmath} 

%%%%%%%

usepackage{tabstackengine}  

TABstackMath

TABstackMathstyle{displaystyle}

renewcommandstacktype{L}

renewcommandstackalignment{r}

setstackgap{L}{24pt}

%%%%%%%%%

usepackage{amsfonts} 

usepackage{amssymb} 

usepackage{mathrsfs}

usepackage{mathtools}

usepackage{hyperref}

usepackage{amsthm}

usepackage[mathscr]{euscript}

usepackage{tikz}

usepackage{pgfplots}

pgfplotsset{compat=newest}

usepackage{wrapfig}

usepackage{latexsym}

usepackage{mathtools}



begin{document}







begin{equation*}

partial_tu(t,x)=left{

begin{array}{l l}

tabbedstackanchor{Bigl(partial_txi^t(x)R'(xi^t(x))-partial_xG(t,x)R(xi^t(x))-R(xi^t(x))int_{xi^t(x)}^tpartial_x^2G(s,Phi(s,t,x))partial_tPhi(s,t,x),mbox{d}s}{+partial_txi^t(x)R(xi^t(x))partial_xG(xi^t(x),1)Bigr)timesexpleft(-int_{xi^t(x)}^tpartial_x 

G(s,Phi_{(t,x)}(s)),mbox{d}sright) },&(t,x)in Omega_1\[20pt]

tabbedstackanchor{Bigl(partial_xG(t,x)u_0(chi^t(x))+G(t,x)partial_xchi^t(x)u'_0(chi^t(x))-u_0(chi^t(x))int_{t_)}^tpartial_x^2G(s,Phi(s,t,x))partial_tPhi(s,t,x),,mbox{d}sBigr)}

{timesexpleft(-int_{t_0}^tpartial_xG(s,Phi_{(t,x)}(s)),mbox{d}sright) },&(t,x)in Omega_2\[24pt]

0,&(t,x)inOmega_3

end{array}

right.

end{equation*}

end{document}

your equation is too huge that can be fit inside text area. as one solution is break math terms into more line:

documentclass{article}

usepackage[margin=25mm]{geometry}

usepackage{mathtools,

            nccmath,

            amssymb}

newcommand{ud}{,mathrm{d}}



usepackage{lipsum} % for dummy text



begin{document}

lipsum[1]

    begin{equation*}medmath{

partial_tu(t,x)=

begin{cases}

begin{multlined}

Bigl(partial_txi^t(x)R'bigl(xi^t(x)bigr) -        \[-3ex]

      partial_x G(t,x)R  bigl(xi^t(x)bigr) -

      R(xi^t(x)) int_{xi^t(x)}^t partial_x^2Gbigl(s,Phi(s,t,x)bigr)

      partial_tPhi(s,t,x)ud s +                      \[-2ex]

      partial_txi^t(x)R bigl(xi^t(x)bigr)

                         partial_x Gbigl(xi^t(x),1bigr)Bigr)

    timesexpbiggl(-int_{xi^t(x)}^t

        partial_x G(s,Phi_{(t,x)}(s))ud sbiggr),

end{multlined}

    &   (t,x)in Omega_1              \[9ex]

begin{multlined}

Bigl(partial_x G(t,x)u_0 bigl(chi^t(x)bigr) +

    G(t,x)partial_x chi^t(x)u'_0bigl(chi^t(x)bigr) -          \[-2ex]

    u_0bigl(chi^t(x)bigr)

    int_{t_)}^t partial_x^2 Gbigl(s,Phi(s,t,x)bigr)

                 partial_tPhi(s,t,x) ud sBigr)

timesexpbiggl(-int_{t_0}^t partial_x G(s,Phi_{(t,x)}(s)) ud sbiggr)

end{multlined}

    &(t,x)in Omega_2              \[7ex]

0,

    &   (t,x)inOmega_3

end{cases}

    }end{equation*}

lipsum[2]

end{document}

which gives:

as you can see, i practically rewrote your equation. instead array i use cases environment (from the amsmath package which is loaded by mathtools), define ud for derivative, repair all your brackets mismatch in wrote whole equation in smaller fonts by use of macro medmath from the package nccmath.