کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4663669 1345271 2013 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Regularity of Solutions to Nonlinear Time Fractional Differential Equation
ترجمه فارسی عنوان
منظم راه حل های معادلات دیفرانسیل تقاربی غیر خطی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

We find an upper viscosity solution and give a proof of the existence-uniqueness in the space C∞(t∈(0,∞);H2s+2(Rn))∩C0(t∈[0,∞);Hs(Rn)), s ∈R, to the nonlinear time fractional equation of distributed order with spatial Laplace operator subject to the Cauchy conditions equation(0.1)∫02p(β)D*β u(x,t)dβ=Δxu(x,t)+f(t,u(t, x)),t≥0,x∈Rn,u(o,x)=ut(0,x)=ψ(x), where Δx is the spatial Laplace operator, D*β is the operator of fractional differentiation in the Caputo sense and the force term F   satisfies the Assumption 1 on the regularity and growth. For the weight function we take a positive-linear combination of delta distributions concentrated at points of interval (0,2) i.e., p(β)=∑k=1mbk δ(β-βk), 0 <βk<2, bk>0, k=1,2,…,m. The regularity of the solution is established in the framework of the space C∞(t∈(0,∞); C∞(Rn))∩Co(t∈[0,∞);C∞(Rn))C∞(t∈(0,∞); C∞(Rn))∩Co(t∈[0,∞);C∞(Rn)) when the initial data belong to the Sobolev space H2s(Rn), s ∈ R.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Acta Mathematica Scientia - Volume 33, Issue 6, November 2013, Pages 1721–1735
نویسندگان
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