【摘要】 一类多维非线性Ｓｏｂｏｌｅｖ－Ｇａｌｐｅｒｎ方程刘亚成，王锋（哈尔滨船舶工程学院数学力学系，哈尔滨１５０００１）ＡＣＬＡＳＳＯＦＭＵＬＴＩＤＩＭＥＮＳＩＯＮＡＬＮＯＮＬＩＮＥＡＲＳＯＢＯＬＥＶ──ＧＡＬＰＥＲＮＥＱＵＡＴＩＯＮＳ￥ＬＩＵＹＡＣＨＥＮＧ...更多还原

【Abstract】 This paper studies the initial-boundary value problem and the initial value problem for a class of nonlinear Sobolev-Galpern equations of arbitrary dimensions ut-△ut=σi(ux)xi.When σi(s) satisfy (H1) and (H2), we obtain the existence and uniqueness of the global generalized solution. When are bounded there exists a unique global strong solution. The nonnegativity of the solution corresponding to the nonnegative initial 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 as σ’(s) is bounded from below, the unique global strong solution can be obtained; furthermore, the smoothness of solution is discussed in detail.更多还原