how to use the partial differential equations to be solved and initial and boundary conditions?

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Unsteady 10 Motion of a Liquid in a Pan 19 -XAX K hexit ) > u (xit ) A slope = 5 It) ( small ) Hexitl = bex, + ) + hex,t ) L Side View W Continuity 26 2 ( hn ) 2t 2x = 0 Momentum 2 ( hn ) + 2 2x ( hurt gb = - Sit high - Iw p W P= wetted perimeter = w tzh Tw = wall shear stress = Cy.z pululBoundary Conditions " (# , t ) = 0 u liz, t ) = 0 Initial Conditions h ( x 1 0 ) = ho u ( x, 0 ) = 0 Define A = hu B = hu2 + 9 62 2 C = - Sttigh + Csulu) ( 8) ] Equations become 2h + 2A = at 2x ( continuity ) 2A- 2B = C ( momentum) at 2x Boundary Conditions Ate It ) = 0 A ( z , t ) = 0 Initial Conditions hex,0) = 17. Acx, 0) = 0