Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities
In this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. The nonlinearity includes a logarithmic term and several power-type terms with nonnegative variable coefficients. Two new necessary and s...
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MDPI AG
2025-01-01
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| author | Milena Dimova Natalia Kolkovska Nikolai Kutev |
| author_facet | Milena Dimova Natalia Kolkovska Nikolai Kutev |
| author_sort | Milena Dimova |
| collection | DOAJ |
| description | In this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. The nonlinearity includes a logarithmic term and several power-type terms with nonnegative variable coefficients. Two new necessary and sufficient conditions for blow up of the weak solutions are established. The first one addresses the blow up of the global weak solutions at infinity. The second necessary and sufficient condition is obtained in the case of strong superlinearity and concerns blow up of the weak solutions for a finite time. Additionally, we derive new sufficient conditions on the initial data that guarantee blow up for either finite or infinite time. A comparison with previous results is also given. |
| format | Article |
| id | doaj-art-36e853977e8f46e09af7cd8339d632a0 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-36e853977e8f46e09af7cd8339d632a02025-01-24T13:40:10ZengMDPI AGMathematics2227-73902025-01-0113231910.3390/math13020319Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type NonlinearitiesMilena Dimova0Natalia Kolkovska1Nikolai Kutev2Faculty of Applied Informatics and Statistics, University of National and World Economy, 8-mi Dekemvri Str., 1700 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, BulgariaIn this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. The nonlinearity includes a logarithmic term and several power-type terms with nonnegative variable coefficients. Two new necessary and sufficient conditions for blow up of the weak solutions are established. The first one addresses the blow up of the global weak solutions at infinity. The second necessary and sufficient condition is obtained in the case of strong superlinearity and concerns blow up of the weak solutions for a finite time. Additionally, we derive new sufficient conditions on the initial data that guarantee blow up for either finite or infinite time. A comparison with previous results is also given.https://www.mdpi.com/2227-7390/13/2/319nonlinear wave equationcombined logarithmic nonlinearitiesblow up at infinityblow up for a finite time |
| spellingShingle | Milena Dimova Natalia Kolkovska Nikolai Kutev Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities Mathematics nonlinear wave equation combined logarithmic nonlinearities blow up at infinity blow up for a finite time |
| title | Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities |
| title_full | Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities |
| title_fullStr | Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities |
| title_full_unstemmed | Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities |
| title_short | Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities |
| title_sort | finite and infinte time blow up of solutions to wave equations with combined logarithmic and power type nonlinearities |
| topic | nonlinear wave equation combined logarithmic nonlinearities blow up at infinity blow up for a finite time |
| url | https://www.mdpi.com/2227-7390/13/2/319 |
| work_keys_str_mv | AT milenadimova finiteandinfintetimeblowupofsolutionstowaveequationswithcombinedlogarithmicandpowertypenonlinearities AT nataliakolkovska finiteandinfintetimeblowupofsolutionstowaveequationswithcombinedlogarithmicandpowertypenonlinearities AT nikolaikutev finiteandinfintetimeblowupofsolutionstowaveequationswithcombinedlogarithmicandpowertypenonlinearities |