کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665011 1633782 2017 54 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An Lq(Lp)-theory for the time fractional evolution equations with variable coefficients
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
An Lq(Lp)-theory for the time fractional evolution equations with variable coefficients
چکیده انگلیسی

We introduce an Lq(Lp)Lq(Lp)-theory for the semilinear fractional equations of the typeequation(0.1)∂tαu(t,x)=aij(t,x)uxixj(t,x)+f(t,x,u),t>0,x∈Rd. Here, α∈(0,2)α∈(0,2), p,q>1p,q>1, and ∂tα is the Caupto fractional derivative of order α  . Uniqueness, existence, and Lq(Lp)Lq(Lp)-estimates of solutions are obtained. The leading coefficients aij(t,x)aij(t,x) are assumed to be piecewise continuous in t and uniformly continuous in x  . In particular aij(t,x)aij(t,x) are allowed to be discontinuous with respect to the time variable. Our approach is based on classical tools in PDE theories such as the Marcinkiewicz interpolation theorem, the Calderon–Zygmund theorem, and perturbation arguments.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 306, 14 January 2017, Pages 123–176
نویسندگان
, , ,