Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1124.35079
Zhou, Yong
Blow-up of solutions to the DGH equation. (English)
[J] J. Funct. Anal. 250, No. 1, 227-248 (2007). ISSN 0022-1236

Summary: Firstly we find best constants for two convolution problems on the unit circle via a variational method. Then we apply the best constants on a nonlinear integrable shallow water equation the Dullin-Gottwald-Holm equation $$\align & u_t-\alpha^2u_{txx}+c_0u_x+3uu_x+\gamma u_{xxx}=\alpha^2(2u_xu_{xx}+uu_{xxx}),\ x\in\bbfR,\ t>0,\\ & u(x,t=0)=u_0(x),x\in\bbfR.\endalign$$ to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions. Finally, we discuss the blow-up phenomena for the nonperiodic case.

MSC 2000:: *35Q53 KdV-like equations
76B15 Wave motions (fluid mechanics)
35A20 Analytic methods (PDE)
37K10 Completely integrable systems etc.

Keywords: best constant; convolution problem; integrable equation; singularity; shallow water equation

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]