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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2605.29619 |
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| _version_ | 1866910269212459008 |
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| author | Ali, Mashkoor |
| author_facet | Ali, Mashkoor |
| contents | In this work, we establish the existence of mass-conserving weak solutions to a nonlinear collision-induced breakage equation in which binary collisions may trigger particle breakup. The result is proved for a class of product-type collision kernels whose small-size behavior is controlled by a power-law function of the form $ω_0(x)\le A_1\,x^\ell$, while no growth restriction is imposed on the large-size factor $ω_\infty$. The qualitative behavior of the solutions depends crucially on the exponent $\ell$ near the origin. Sublinear growth corresponding to $\ell<\tfrac12$ yields existence only on finite time intervals, whereas superlinear growth corresponding to $\ell>\tfrac12$ ensures global-in-time existence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29619 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Class of Continuous Collision-Induced Breakage Equation Ali, Mashkoor Analysis of PDEs 45K05, 35A01 In this work, we establish the existence of mass-conserving weak solutions to a nonlinear collision-induced breakage equation in which binary collisions may trigger particle breakup. The result is proved for a class of product-type collision kernels whose small-size behavior is controlled by a power-law function of the form $ω_0(x)\le A_1\,x^\ell$, while no growth restriction is imposed on the large-size factor $ω_\infty$. The qualitative behavior of the solutions depends crucially on the exponent $\ell$ near the origin. Sublinear growth corresponding to $\ell<\tfrac12$ yields existence only on finite time intervals, whereas superlinear growth corresponding to $\ell>\tfrac12$ ensures global-in-time existence. |
| title | On a Class of Continuous Collision-Induced Breakage Equation |
| topic | Analysis of PDEs 45K05, 35A01 |
| url | https://arxiv.org/abs/2605.29619 |