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\\Omega, ~~t>0,\n  w_t=D_2\\Delta w+\\gamma u-\\delta w, &x\\in \\Omega, ~~t>0,\\\\ u(x,0)=u_0(x),~v(x,0)= v_0(x), w(x,0)= w_0(x) & x\\in \\Omega, \\end{cases} \\end{equation} in a bounded domain $\\Omega\\subset \\R^2$ with smooth boundary subject to homogeneous Neumann boundary conditions. %The parameters 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