Boundary-value problems for certain quasilinear nonuniformly parabolic equations with nonclassical degeneracies (Q1103781)

The solvability of boundary value problems for quasilinear non-uniformly parabolic equations with non-classical degenerations \(u_ t=(\partial /\partial x)\omega (u_ x)+f(u)\), where \(\omega (u_ x)=((1+u_ x)^{2n+1}-1)/(1+u_ x)^{2n+1}\), \(n=0,1,2,..\). or \(\omega (u_ x)=e^{u_ x}\), \(f\in C^ 1\), f'(u)\(\leq 0\), \(f(0)=0\) is studied.