Cauchy problem for a linear hyperbolic equation of the second order
The definition of hyperbolic equation by a prescribed vector field is introduced for linear differential equation of the second order. The Cauchy problem with prescribed boundary conditions is considered for such equations. The theorems of existence and uniqueness of a strong solution to the given...
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Vilnius Gediminas Technical University
2006-09-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/9618 |
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doaj-fc23365ef5964b0ab4e246eb76a689c62021-07-02T10:57:23ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102006-09-0111310.3846/13926292.2006.9637318Cauchy problem for a linear hyperbolic equation of the second orderV. I. Korzyuk0E.S. Cheb1Belarussian State University , Skoriny 4, Minsk, 220050, BelarusBelarussian State University , Skoriny 4, Minsk, 220050, Belarus The definition of hyperbolic equation by a prescribed vector field is introduced for linear differential equation of the second order. The Cauchy problem with prescribed boundary conditions is considered for such equations. The theorems of existence and uniqueness of a strong solution to the given problem are proved by the method of energy inequalities and mollifiers with variable step. Key words: hyperbolic equation, Cauchy problem, strong solution, energy inequality, mollifiers. First Published Online: 14 Oct 2010 https://journals.vgtu.lt/index.php/MMA/article/view/9618- |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
V. I. Korzyuk E.S. Cheb |
| spellingShingle |
V. I. Korzyuk E.S. Cheb Cauchy problem for a linear hyperbolic equation of the second order Mathematical Modelling and Analysis - |
| author_facet |
V. I. Korzyuk E.S. Cheb |
| author_sort |
V. I. Korzyuk |
| title |
Cauchy problem for a linear hyperbolic equation of the second order |
| title_short |
Cauchy problem for a linear hyperbolic equation of the second order |
| title_full |
Cauchy problem for a linear hyperbolic equation of the second order |
| title_fullStr |
Cauchy problem for a linear hyperbolic equation of the second order |
| title_full_unstemmed |
Cauchy problem for a linear hyperbolic equation of the second order |
| title_sort |
cauchy problem for a linear hyperbolic equation of the second order |
| publisher |
Vilnius Gediminas Technical University |
| series |
Mathematical Modelling and Analysis |
| issn |
1392-6292 1648-3510 |
| publishDate |
2006-09-01 |
| description |
The definition of hyperbolic equation by a prescribed vector field is introduced for linear differential equation of the second order. The Cauchy problem with prescribed boundary conditions is considered for such equations. The theorems of existence and uniqueness of a strong solution to the given problem are proved by the method of energy inequalities and mollifiers with variable step. Key words: hyperbolic equation, Cauchy problem, strong solution, energy inequality, mollifiers.
First Published Online: 14 Oct 2010
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| url |
https://journals.vgtu.lt/index.php/MMA/article/view/9618 |
| work_keys_str_mv |
AT vikorzyuk cauchyproblemforalinearhyperbolicequationofthesecondorder AT escheb cauchyproblemforalinearhyperbolicequationofthesecondorder |
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1721331626477092864 |