CAJ | 학술논문

本文研究了一类具有非线性边界流的双重退化抛物型方程,该方程可用来描述多孔介质中的非牛顿渗流现象,可以描述气体或液体在多孔介质中的流动,具有广泛的实际背景.通过构造不同的自相似上、下解得到了方程的临界指标,即整体存在指标po和临界Fujita指标pc.主要结果为:当0＜p≤po时,方程存在整体解;当po＜p＜pc时,方程不存在非负非平凡整体解;当p＞pc时,对于小初值方程存在整体解,对于大初值不存在整体解.
본문연구료일류구유비선성변계류적쌍중퇴화포물형방정,해방정가용래묘술다공개질중적비우돈삼류현상,가이묘술기체혹액체재다공개질중적류동,구유엄범적실제배경.통과구조불동적자상사상、하해득도료방정적림계지표,즉정체존재지표po화림계Fujita지표pc.주요결과위:당0＜p≤po시,방정존재정체해;당po＜p＜pc시,방정불존재비부비평범정체해;당p＞pc시,대우소초치방정존재정체해,대우대초치불존재정체해.
This paper studies the critical exponents of a doubly degenerate parabolic equation with nonlinear boundary flux. The equation can be used to describe the nonstationary flow in a porous medium of fluids with a power dependence of the tangential stress on the velocity of the displacement under polytropic conditions. This study is thus meaningful in various branches of applied mathematics. We obtained the global existence exponent po and critical Fujita exponent pc by constructing various self-similar supersolutions and subsolutions of the objective doubly degenerate parabolie equation. The main results of this paper are as follows the equation exists global solutions if 0 ＜ p ≤ po; the equation does not exist nontrivial and nonnegative global solutions if po ＜ p ＜ pc; the equation exists global solutions for small initial valus while does not exists global solutions otherwise if p ＞pc.