Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order)

被引：8

作者：

Van Bockstal, Karel ^{[1
]}

机构：

[1] Univ Ghent, Res Grp NaM2, Dept Elect & Informat Syst, Krijgslaan 281, B-9000 Ghent, Belgium

来源：

MATHEMATICS | 2020年 / 8卷 / 08期

关键词：

time-fractional wave equation; distributed-order; non-autonomous; time discretization; existence; uniqueness; DIFFERENCE-SCHEMES;

D O I：

10.3390/math8081283

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study an initial-boundary value problem for a fractional wave equation of time distributed-order with a nonlinear source term. The coefficients of the second order differential operator are dependent on the spatial and time variables. We show the existence of a unique weak solution to the problem under low regularity assumptions on the data, which includes weakly singular solutions in the class of admissible problems. A similar result holds true for the fractional wave equation with Caputo fractional derivative.

引用

页数：16

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