Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 25, Issue 1, Pages 63-77Publisher
SPRINGER
DOI: 10.1007/s00526-005-0358-1
Keywords
best constant; convolution problem; rod equation; singularity
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In this paper, firstly we find the best constant for a convolution problem on the unit circle via a variational method. Then we apply the best constant on a nonlinear rod equation to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions.
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