The nonexistence of global solutions for a time fractional nonlinear Schrödinger equation without gauge invariance
详细信息    查看全文
文摘
In this paper, we study the following time fractional Schr&ouml;dinger equation where k to view the MathML source">0<α<1, k to view the MathML source">iα denotes the principal value of k to view the MathML source">iα, k to view the MathML source">T>0, k to view the MathML source">λ∈C∖{0}, k to view the MathML source">p>1, k to view the MathML source">u(t,x) is a complex-valued function, and w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089396591630252X&_mathId=si9.gif&_user=111111111&_pii=S089396591630252X&_rdoc=1&_issn=08939659&md5=4be8077617b25440d2744a224cc1c946">width="35" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S089396591630252X-si9.gif"> denotes Caputo fractional derivative of order k to view the MathML source">α. We prove that the problem admits no global weak solution with suitable initial data when k to view the MathML source">1<p<1+2∕N by using the test function method, and also give some conditions which imply the problem has no global weak solution for every k to view the MathML source">p>1.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700