documentclass[border=2pt,convert={ghostscript, density={4000}}, varwidth]{standalone}
usepackage{amsmath}

begin{document}
    begin{align}
        partial_tx(z,t) &=
        Lambda(z)partial_z^2x(z,t) + Phi(z)partial_zx(z,t) + A(z)x(z,t)
        label{pdes}\
        partial_zx(0,t) &= Q_0x(0,t),\
        partial_zx(1,t) &= Q_1x(1,t) + u(t),
        end{align}
end{document}