Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters

Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters PDF Author: Giao Ky Duong
Publisher:
ISBN: 9781470474812
Category : Differential equations, Partial
Languages : en
Pages : 0

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Book Description
We construct a solution for the Complex Ginzburg-Landau (CGL) equation in a general critical case, which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile. In the first part, we formally construct a blow-up solution. In the second part we give the rigorous proof. The proof relies on the reduction of the problem to a finite dimensional one, and the use of index theory to conclude. The interpretation of the parameters of the finite dimension problem in terms of the blow-up point and time allows to prove the stability of the constructed solution. We would like to mention that the asymptotic profile of our solution is different from previously known profiles for CGL or for the semilinear heat equation.

Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters

Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters PDF Author: Giao Ky Duong
Publisher:
ISBN: 9781470474812
Category : Differential equations, Partial
Languages : en
Pages : 0

Get Book Here

Book Description
We construct a solution for the Complex Ginzburg-Landau (CGL) equation in a general critical case, which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile. In the first part, we formally construct a blow-up solution. In the second part we give the rigorous proof. The proof relies on the reduction of the problem to a finite dimensional one, and the use of index theory to conclude. The interpretation of the parameters of the finite dimension problem in terms of the blow-up point and time allows to prove the stability of the constructed solution. We would like to mention that the asymptotic profile of our solution is different from previously known profiles for CGL or for the semilinear heat equation.

Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters

Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters PDF Author: Giao Ky Duong
Publisher: American Mathematical Society
ISBN: 1470461218
Category : Mathematics
Languages : en
Pages : 104

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Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits

Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits PDF Author: Pablo Candela
Publisher: American Mathematical Society
ISBN: 1470465485
Category : Mathematics
Languages : en
Pages : 114

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Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume

Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume PDF Author: Roelof Bruggeman
Publisher: American Mathematical Society
ISBN: 1470465450
Category : Mathematics
Languages : en
Pages : 186

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On Medium-Rank Lie Primitive and Maximal Subgroups of Exceptional Groups of Lie Type

On Medium-Rank Lie Primitive and Maximal Subgroups of Exceptional Groups of Lie Type PDF Author: David A. Craven
Publisher: American Mathematical Society
ISBN: 147046702X
Category : Mathematics
Languages : en
Pages : 226

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Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster

Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster PDF Author: Alexander Bors
Publisher: American Mathematical Society
ISBN: 1470465442
Category : Mathematics
Languages : en
Pages : 108

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Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems

Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems PDF Author: Tudor S. Ratiu
Publisher: American Mathematical Society
ISBN: 147046439X
Category : Mathematics
Languages : en
Pages : 102

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Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds

Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds PDF Author: Hiroshi Kihara
Publisher: American Mathematical Society
ISBN: 1470465426
Category : Mathematics
Languages : en
Pages : 144

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Analyticity Results in Bernoulli Percolation

Analyticity Results in Bernoulli Percolation PDF Author: Agelos Georgakopoulos
Publisher: American Mathematical Society
ISBN: 1470467054
Category : Mathematics
Languages : en
Pages : 114

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Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity

Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity PDF Author: Olivier Bernardi
Publisher: American Mathematical Society
ISBN: 1470466996
Category : Mathematics
Languages : en
Pages : 188

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