Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters PDF Download
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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.
Author: Giao Ky Duong
Publisher:
ISBN: 9781470474812
Category : Differential equations, Partial
Languages : en
Pages : 0
Get Book
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.
Author: Giao Ky Duong
Publisher: American Mathematical Society
ISBN: 1470461218
Category : Mathematics
Languages : en
Pages : 104
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Author: Pablo Candela
Publisher: American Mathematical Society
ISBN: 1470465485
Category : Mathematics
Languages : en
Pages : 114
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Author: Roelof Bruggeman
Publisher: American Mathematical Society
ISBN: 1470465450
Category : Mathematics
Languages : en
Pages : 186
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Author: David A. Craven
Publisher: American Mathematical Society
ISBN: 147046702X
Category : Mathematics
Languages : en
Pages : 226
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Author: Alexander Bors
Publisher: American Mathematical Society
ISBN: 1470465442
Category : Mathematics
Languages : en
Pages : 108
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Author: Tudor S. Ratiu
Publisher: American Mathematical Society
ISBN: 147046439X
Category : Mathematics
Languages : en
Pages : 102
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Author: Hiroshi Kihara
Publisher: American Mathematical Society
ISBN: 1470465426
Category : Mathematics
Languages : en
Pages : 144
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Author: Agelos Georgakopoulos
Publisher: American Mathematical Society
ISBN: 1470467054
Category : Mathematics
Languages : en
Pages : 114
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Author: Olivier Bernardi
Publisher: American Mathematical Society
ISBN: 1470466996
Category : Mathematics
Languages : en
Pages : 188
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