Existence And Blow-up Of Solutions Of A Class Of Multidimensional Nonlinear Parabolic Equations

In this paper, we consider the initial boundary value problem for a class of multidimensional nonlinear parabolic equationΩ(?)Rⁿ is a propriate bounded domain and f∈C. And the existence of solution is established. Whenσ_i(s)(1≤i≤n), f(u) satisfy(H₁)σ_i, f∈C, (?)k, satisfy (?)_i(s)=σ_i(s)-ks-σ_i(0) is not decreasing function,wherek, A, A₁, B, B₁ andα,γare constant, we obtain the existence and uniqueness of the global generalized solution.Whenσ′_i(s)(1≤i≤n),f'(u)are bonuded there exists a unique global strong solution.The nonnegativity of the solution corresponding to the nonnegative initial boundary value, the asymptotic behavior and the blow-up of the solution are also discussed.For the case of one dimension, more general boundary conditions are considered;so long asσ'(s), f'(u) is bounded from below, the unique global strong solution can be obtained;furthermore, the smoothness of solution is discussed in detail.