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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2509.06671 |
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| _version_ | 1866908524713345024 |
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| author | Longen, Luis Gustavo |
| author_facet | Longen, Luis Gustavo |
| contents | In this paper, we study a mixed wave-plate equation with rotational inertia, fractional damping and memory non-linearity. This research is a non-existence counterpart to a paper by D'Abbicco and Longen, in search of the critical exponent for the global in-time existence of small data solutions to the Cauchy problem for a mixed wave-plate equation, with a rotational inertia and a non-integer dissipation term and a memory-type non-linearity. We employ a modified test function argument to show that there are arbitrarily small initial data for which there are no solutions for the problem in the subcritical case. Additionally, we show non-existence of global solutions in the critical case when the memory exponent is greater than (n-2)/n. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06671 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Existence of Solutions for a Fourth-Order Structurally Damped Equation Under Nonlinear Memory Effect Longen, Luis Gustavo Analysis of PDEs 35L25 (Primary), 26A33, 74K20 In this paper, we study a mixed wave-plate equation with rotational inertia, fractional damping and memory non-linearity. This research is a non-existence counterpart to a paper by D'Abbicco and Longen, in search of the critical exponent for the global in-time existence of small data solutions to the Cauchy problem for a mixed wave-plate equation, with a rotational inertia and a non-integer dissipation term and a memory-type non-linearity. We employ a modified test function argument to show that there are arbitrarily small initial data for which there are no solutions for the problem in the subcritical case. Additionally, we show non-existence of global solutions in the critical case when the memory exponent is greater than (n-2)/n. |
| title | Non-Existence of Solutions for a Fourth-Order Structurally Damped Equation Under Nonlinear Memory Effect |
| topic | Analysis of PDEs 35L25 (Primary), 26A33, 74K20 |
| url | https://arxiv.org/abs/2509.06671 |