| We establish the global existence of solutions to a class of differential equations of the form: wt+sxwx x=0, st=w-s &parl0;sxx &parr0;x-s2x x+gb&parl0;w-s&parr0; q, inspired by a system first solved by Choi, Groulx, and Lui in [1]. Here x and gb are positive constants. In the first case we will consider value of q > 1 with w(x, 0) = b 0 > 0. In the second case we set q = 1, but w(x, 0) > 0 and non-constant so that a coupled hyperbolic-parabolic has to be studied. |
