【摘要】 在本文中,我们利用抛物正则化和椭圆正则化方法,在一定条件下,证明了一类二阶拟线性弱耦合退缩方程组的初值问题和边值问题在BV空间中广义解的存在性。进而,在较强的条件下,证明了所得的广义解还是唯一的。更多还原

【Abstract】 In this paper, we investigate the initial and boundary value problems for a class of quasilinear degenerate systems. We first establish some maximum principles for linear systems. Then we prove the existence of generalized solutions in BV space for a class of quasilinear degenerate parabolic systems. Finally, we considered the initial and boundary value problems for quasilinear degenerate systems coupled by parabolic equations and elliptic equations, and the solvability is established in BV space. The same result is true for quasilinear degenerate elliptic systems. Thus we extend the results in [1] to the quasilinear case.更多还原