SOLUTIONS TO POLYTROPIC FILTRATION EQUATIONS WITH A CONVECTION TERM

We introduce a new type of the weak solution of the polytropic filtration equations with a convection term, ut = div(a(x)|u|(a)|del u|(p-2)del u)+partial derivative b(i)(u(m))/partial derivative x(i). Here, Omega subset of R-N is a domain with a C-2 smooth boundary partial derivative Omega, a(x) is an element of C-1((Omega) over bar), p > 1, m = 1+alpha/p-1, alpha > 0, a(x) > 0 when x is an element of Omega and a(x) = 0 when x is an element of partial derivative Omega. Since the equation is degenerate on the boundary, its weak solutions may lack the needed regularity to have a trace on the boundary. The main aim of the paper is to establish the stability of the weak solution without any boundary value condition.