In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj （α^ij （x, t, u）Diψ（u）） ＋b^i （t, u）Diu＋C（x, t, u） = 0, and obtain the existence, un...In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj （α^ij （x, t, u）Diψ（u）） ＋b^i （t, u）Diu＋C（x, t, u） = 0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.展开更多
The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of pertu...The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of perturbed first-order ordinary dif- ferential equations systems and approximate solutions are obtained by using these symmetries.展开更多
基金Foundation item： Supported by National Science Foundation of China（10572156） Supported by Natural Science Foundation of Henan Province（0211010900） Supported by National Science Foundation of Department of Education of Henan Province（200510465001）
文摘In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj （α^ij （x, t, u）Diψ（u）） ＋b^i （t, u）Diu＋C（x, t, u） = 0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.
基金Supported by the National Natural Science Foundation of China(11326167,11226195)the Natural Science Foundation of Henan Province(142300410354)Foundation of Henan Educational Committee(13A110119,15B110012)
文摘The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of perturbed first-order ordinary dif- ferential equations systems and approximate solutions are obtained by using these symmetries.
