Comparison theorems for nonlinear evolution equations and their application to the investigation of the dependence of the solutions of the equation ut=δϕ(u) ON ϕ and on the boundary conditions

One obtains estimates of the form[Figure not available: see fulltext.], where u. Ν are generalized solutions of the equations du/dt=Au, du/dt=Bu while A, B are non-linear, m-dissipative operators in a Banach space, and there exists an operator P:D(A)→D(B), such that {norm of matrix}Pw · W{norm of matrix}+{norm of matrix}BPw -Aw{norm of matrix}≤δ, uniformly on some set w. These results are applied to the investigation of the dependence of the solutions of the Cauchy, Dirichlet problems and of the problem with the boundary condition -du/dn=β(u) for the equation u₁=Δφ{symbol}(u) on the continuous nondecreasing functions φ{symbol} and Β.