A Time-Fractional Differential Inequality of Sobolev Type on an Annulus

被引:0
作者
Alshabanat, Amal [1 ]
Almoalim, Eman [1 ]
Jleli, Mohamed [2 ]
Samet, Bessem [2 ]
机构
[1] Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, Riyadh 11671, Saudi Arabia
[2] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia
关键词
differential inequalities of Sobolev-type; Caputo fractional derivative; weak solution; nonexistence; CRITICAL EXPONENTS; GLOBAL-SOLUTIONS; BLOW-UP; EQUATIONS; NONEXISTENCE;
D O I
10.3390/axioms12100993
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard derivatives. The goal of this paper is to study the nonexistence of weak solutions to a time-fractional differential inequality of Sobolev-type. Namely, we give sufficient conditions for the nonexistence or equivalently necessary conditions for the existence. Our method makes use of the nonlinear capacity method, which consists in making an appropriate choice of test functions in the weak formulation of the problem. This technique has been employed in previous papers for some classes of time-fractional differential inequalities of Sobolev-type posed on the whole space RN. The originality of this work is that the considered problem is posed on an annulus domain, which leads to some difficulties concerning the choice of adequate test functions.
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页数:11
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