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Zeros of complex caloric functions and singularities of complex viscous Burgers equation
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P. Poláčik
Published/Copyright:
May 13, 2008
Abstract
We show that the viscous Burgers equation ut + uux = uxx considered for complex valued functions u develops finite-time singularities from compactly supported smooth data. By means of the Cole-Hopf transformation, the singularities of u are related to zeros of complex-valued solutions v of the heat equation vt = vxx. We prove that such zeros are isolated if they are not present in the initial data.
Received: 2007-02-01
Published Online: 2008-05-13
Published in Print: 2008-March
© Walter de Gruyter
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Articles in the same Issue
- Smooth localized parametric resonance for wave equations
- Estimates and regularity results for the DiPerna-Lions flow
- Sur le nombre d'éléments exceptionnels d'une base additive
- Alder's conjecture
- Local monotonicity and mean value formulas for evolving Riemannian manifolds
- Projective-injective modules, Serre functors and symmetric algebras
- Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
- Zeros of complex caloric functions and singularities of complex viscous Burgers equation
- Generalised form of a conjecture of Jacquet and a local consequence
