不連続な係数を持つ強退化放物型方程式に対する初期値問題について
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概要
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In this papaer, we consider the initial value problem for a strongly degenerate parabolic equation of the form ut + ∇・A(x,t,u) + B(x,t,u) = Δβ(u). Since equations of this form are linear combinations of time-dependent conservation laws and porous medium type equations, it is interesting to investigate interactions between singularities of solutions associated with the two different kinds of nonlinearities. However either of the part of conservation laws and that of porous medium type diffusion term may not be treated as a purterbation of the other. In particular, we consider the strongly degenerate parabolic equations which have discontinuous coefficients. Our objective here is to establish the unique existence of weak solutions using the strong pre-compactness theorem derived by Panov^7).
- 2012-03-01
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