Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise
The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematic...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2023-01-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/30563 |
| _version_ | 1797953822758273024 |
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| author | Muhammad Ozair Ahmed Rishi Naeem Muhammad Akhtar Tarar Muhammad Sajid Iqbal Mustafa Inc Farkhanda Afzal |
| author_facet | Muhammad Ozair Ahmed Rishi Naeem Muhammad Akhtar Tarar Muhammad Sajid Iqbal Mustafa Inc Farkhanda Afzal |
| author_sort | Muhammad Ozair Ahmed |
| collection | DOAJ |
| description |
The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots.
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| first_indexed | 2024-04-10T23:08:09Z |
| format | Article |
| id | doaj.art-b70ae49d95b9447ab34c605ee055275f |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-10T23:08:09Z |
| publishDate | 2023-01-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-b70ae49d95b9447ab34c605ee055275f2023-01-13T09:44:27ZengVilnius University PressNonlinear Analysis1392-51132335-89632023-01-0128210.15388/namc.2023.28.30563Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noiseMuhammad Ozair Ahmed0Rishi Naeem1Muhammad Akhtar Tarar2Muhammad Sajid Iqbal3Mustafa Inc4Farkhanda Afzal5The University of LahoreMilitary College of Signals, NUSTThe University of LahoreMilitary College of Signals, NUSTFirat UniversityMilitary College of Signals, NUST The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots. https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/30563singular partial differential equationsnoise functionexact solutionsSchauder’s fixed point theorema priori estimates |
| spellingShingle | Muhammad Ozair Ahmed Rishi Naeem Muhammad Akhtar Tarar Muhammad Sajid Iqbal Mustafa Inc Farkhanda Afzal Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise Nonlinear Analysis singular partial differential equations noise function exact solutions Schauder’s fixed point theorem a priori estimates |
| title | Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise |
| title_full | Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise |
| title_fullStr | Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise |
| title_full_unstemmed | Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise |
| title_short | Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise |
| title_sort | existence theories and exact solutions of nonlinear pdes dominated by singularities and time noise |
| topic | singular partial differential equations noise function exact solutions Schauder’s fixed point theorem a priori estimates |
| url | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/30563 |
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