Two parameter singular perturbation problems for sine-Gordon type equations
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2022-10-20 13:38
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PERJAN, Andrei; RUSU, Galina. Two parameter singular perturbation problems for sine-Gordon type equations. In: Mathematics and IT: Research and Education. 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, pp. 68-69.
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Mathematics and IT: Research and Education 2021
Conferința "Mathematics and IT: Research and Education "
Chişinău, Moldova, 1-3 iulie 2021

Two parameter singular perturbation problems for sine-Gordon type equations


Pag. 68-69

Perjan Andrei, Rusu Galina
 
State University of Moldova
 
Disponibil în IBN: 30 iunie 2021


Rezumat

formulaThe interest for the sine-Gordon equation is explained by the various applications in differential geometry and engineering, including junctions between two superconductors, the motion of rigid pendular attached to a stretched wire, dislocations in crystals, nonlinear optics. Using similar specific techniques, the functional framework of the Sobolev space H1 0 (­) and the properties of the strongly elliptic operator, we investigate the behavior of solutions u"± to the problem (P"±) in two different cases: (i) " ! 0 and ± ¸ ±0 > 0, relative to the solutions to the following unperturbed system:formulaThe problem (P"±) is the abstract model of singularly perturbed problems of hyperbolic-parabolic type in the case (i) and of the hyperbolic-parabolic-elliptic type in the case (ii).