Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition
This work is concerned with a mixed boundary value problem for the semilinear parabolic equation with a memory term and generalized Lewis functions which depends on both spacial variable and time. Under suitable conditions, we prove the existence and uniqueness of global solutions and the energy fun...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/532935 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560547616260096 |
|---|---|
| author | Zhong Bo Fang Liru Qiu |
| author_facet | Zhong Bo Fang Liru Qiu |
| author_sort | Zhong Bo Fang |
| collection | DOAJ |
| description | This work is concerned with a mixed boundary value problem for the semilinear parabolic equation with a memory term and generalized Lewis functions which depends on both spacial variable and time. Under suitable conditions, we prove the existence and uniqueness of global solutions and the energy functional decaying exponentially or polynomially to zero as the time goes to infinity by introducing brief Lyapunov function and precise priori estimates. |
| format | Article |
| id | doaj-art-b40701a485b74058a7a0946f71db5b0d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b40701a485b74058a7a0946f71db5b0d2025-02-03T01:27:18ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/532935532935Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary ConditionZhong Bo Fang0Liru Qiu1School of Mathematical Sciences, Ocean University of China, Qingdao 266100, ChinaSchool of Mathematical Sciences, Ocean University of China, Qingdao 266100, ChinaThis work is concerned with a mixed boundary value problem for the semilinear parabolic equation with a memory term and generalized Lewis functions which depends on both spacial variable and time. Under suitable conditions, we prove the existence and uniqueness of global solutions and the energy functional decaying exponentially or polynomially to zero as the time goes to infinity by introducing brief Lyapunov function and precise priori estimates.http://dx.doi.org/10.1155/2013/532935 |
| spellingShingle | Zhong Bo Fang Liru Qiu Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition Abstract and Applied Analysis |
| title | Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition |
| title_full | Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition |
| title_fullStr | Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition |
| title_full_unstemmed | Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition |
| title_short | Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition |
| title_sort | global existence and uniform energy decay rates for the semilinear parabolic equation with a memory term and mixed boundary condition |
| url | http://dx.doi.org/10.1155/2013/532935 |
| work_keys_str_mv | AT zhongbofang globalexistenceanduniformenergydecayratesforthesemilinearparabolicequationwithamemorytermandmixedboundarycondition AT liruqiu globalexistenceanduniformenergydecayratesforthesemilinearparabolicequationwithamemorytermandmixedboundarycondition |