Consider the initial boundary value problem of the strong degenerate parabolic equation ?_(xx)u + u?_yu-?_tu = f(x, y, t, u),(x, y, t) ∈ Q_T = Ω×(0, T)with a homogeneous boundary condition. By introducing a new...Consider the initial boundary value problem of the strong degenerate parabolic equation ?_(xx)u + u?_yu-?_tu = f(x, y, t, u),(x, y, t) ∈ Q_T = Ω×(0, T)with a homogeneous boundary condition. By introducing a new kind of entropy solution, according to Oleinik rules, the partial boundary condition is given to assure the well-posedness of the problem. By the parabolic regularization method, the uniform estimate of the gradient is obtained, and by using Kolmogoroff 's theorem, the solvability of the equation is obtained in BV(Q_T) sense. The stability of the solutions is obtained by Kruzkov's double variables method.展开更多
基金supported by the National Natural Science Foundation of China(No.11371297)the Science Foundation of Xiamen University of Technology(No.XYK201448)
文摘Consider the initial boundary value problem of the strong degenerate parabolic equation ?_(xx)u + u?_yu-?_tu = f(x, y, t, u),(x, y, t) ∈ Q_T = Ω×(0, T)with a homogeneous boundary condition. By introducing a new kind of entropy solution, according to Oleinik rules, the partial boundary condition is given to assure the well-posedness of the problem. By the parabolic regularization method, the uniform estimate of the gradient is obtained, and by using Kolmogoroff 's theorem, the solvability of the equation is obtained in BV(Q_T) sense. The stability of the solutions is obtained by Kruzkov's double variables method.
