Uniqueness of piecewise smooth weak solutions of multidimensional degenerate parabolic equations

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

We study the degenerate parabolic equation ut + ∇ · f = ∇ · (Q∇u) + g, where (x, t) ∈ ℝN × ℝ+, the flux f, the viscosity coefficient Q, and the source term g depend on (x, t, u) and Q is nonnegative definite. Due to the possible degeneracy, weak solutions are considered. In general, these solutions are not uniquely determined by the initial data and, therefore, additional conditions must be imposed in order to guarantee uniqueness. We consider here the subclass of piecewise smooth weak solutions, i.e., continuous solutions which are C2-smooth everywhere apart from a closed nowhere dense collection of smooth manifolds. We show that the solution operator is L1-stable in this subclass and, consequently, that piecewise smooth weak solutions are uniquely determined by the initial data.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)598-608
عدد الصفحات11
دوريةJournal of Mathematical Analysis and Applications
مستوى الصوت210
رقم الإصدار2
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 15 يونيو 1997
منشور خارجيًانعم

ملاحظة ببليوغرافية

Funding Information:
*Research supported by ONR Grant N00014-92-J-1890.

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