On a Mixed Problem for a Constant Coefficient Second-Order System
<p/> <p>The paper is devoted to the study of an initial boundary value problem for a linear second-order differential system with constant coefficients. The first part of the paper is concerned with the existence of the solution to a boundary value problem for the second-order differenti...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.boundaryvalueproblems.com/content/2010/526917 |
| _version_ | 1818551988714995712 |
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| author | Cavazzoni Rita |
| author_facet | Cavazzoni Rita |
| author_sort | Cavazzoni Rita |
| collection | DOAJ |
| description | <p/> <p>The paper is devoted to the study of an initial boundary value problem for a linear second-order differential system with constant coefficients. The first part of the paper is concerned with the existence of the solution to a boundary value problem for the second-order differential system, in the strip <inline-formula> <graphic file="1687-2770-2010-526917-i1.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2010-526917-i2.gif"/></inline-formula> is a suitable positive number. The result is proved by means of the same procedure followed in a previous paper to study the related initial value problem. Subsequently, we consider a mixed problem for the second-order constant coefficient system, where the space variable varies in <inline-formula> <graphic file="1687-2770-2010-526917-i3.gif"/></inline-formula> and the time-variable belongs to the bounded interval <inline-formula> <graphic file="1687-2770-2010-526917-i4.gif"/></inline-formula>, with <inline-formula> <graphic file="1687-2770-2010-526917-i5.gif"/></inline-formula> sufficiently small in order that the operator satisfies suitable energy estimates. We obtain by superposition the existence of a solution <inline-formula> <graphic file="1687-2770-2010-526917-i6.gif"/></inline-formula>, by studying two related mixed problems, whose solutions exist due to the results proved for the Cauchy problem in a previous paper and for the boundary value problem in the first part of this paper.</p> |
| first_indexed | 2024-12-12T09:07:13Z |
| format | Article |
| id | doaj.art-697ec0bfc9c14828a358ba01cc711f3b |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-12T09:07:13Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-697ec0bfc9c14828a358ba01cc711f3b2022-12-22T00:29:37ZengSpringerOpenBoundary Value Problems1687-27621687-27702010-01-0120101526917On a Mixed Problem for a Constant Coefficient Second-Order SystemCavazzoni Rita<p/> <p>The paper is devoted to the study of an initial boundary value problem for a linear second-order differential system with constant coefficients. The first part of the paper is concerned with the existence of the solution to a boundary value problem for the second-order differential system, in the strip <inline-formula> <graphic file="1687-2770-2010-526917-i1.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2010-526917-i2.gif"/></inline-formula> is a suitable positive number. The result is proved by means of the same procedure followed in a previous paper to study the related initial value problem. Subsequently, we consider a mixed problem for the second-order constant coefficient system, where the space variable varies in <inline-formula> <graphic file="1687-2770-2010-526917-i3.gif"/></inline-formula> and the time-variable belongs to the bounded interval <inline-formula> <graphic file="1687-2770-2010-526917-i4.gif"/></inline-formula>, with <inline-formula> <graphic file="1687-2770-2010-526917-i5.gif"/></inline-formula> sufficiently small in order that the operator satisfies suitable energy estimates. We obtain by superposition the existence of a solution <inline-formula> <graphic file="1687-2770-2010-526917-i6.gif"/></inline-formula>, by studying two related mixed problems, whose solutions exist due to the results proved for the Cauchy problem in a previous paper and for the boundary value problem in the first part of this paper.</p>http://www.boundaryvalueproblems.com/content/2010/526917 |
| spellingShingle | Cavazzoni Rita On a Mixed Problem for a Constant Coefficient Second-Order System Boundary Value Problems |
| title | On a Mixed Problem for a Constant Coefficient Second-Order System |
| title_full | On a Mixed Problem for a Constant Coefficient Second-Order System |
| title_fullStr | On a Mixed Problem for a Constant Coefficient Second-Order System |
| title_full_unstemmed | On a Mixed Problem for a Constant Coefficient Second-Order System |
| title_short | On a Mixed Problem for a Constant Coefficient Second-Order System |
| title_sort | on a mixed problem for a constant coefficient second order system |
| url | http://www.boundaryvalueproblems.com/content/2010/526917 |
| work_keys_str_mv | AT cavazzonirita onamixedproblemforaconstantcoefficientsecondordersystem |