Blow-up of solutions to the Euler-Poisson-Darbox equation with critical power nonlinearity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917362778767360 |
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| author | Fan, Mengting Lai, Ning-An Takamura, Hiroyuki |
| author_facet | Fan, Mengting Lai, Ning-An Takamura, Hiroyuki |
| contents | In our recent precious work, we established the finite time blow up result and upper bound of lifespan estimate to the singular Cauchy problem of semilinear Euler-Poisson-Darboux equation in R^n with subcritical power type nonlinearity. By introducing an improved test function, we obtain an enhanced lower bound for the functional including the spacetime integral of the nonlinear term with an additional logarithmic growth, which finally yields the blow up result and upper bound of lifespan estimate for the corresponding Cauchy problem with "critical" nonlinear power. And this gives some partial answer to the open problem 1 posed by D'Abbicco (J. Differential Equations 286 (2021), 531-556). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blow-up of solutions to the Euler-Poisson-Darbox equation with critical power nonlinearity Fan, Mengting Lai, Ning-An Takamura, Hiroyuki Analysis of PDEs primary: 35L71, secondary: 35Q05 In our recent precious work, we established the finite time blow up result and upper bound of lifespan estimate to the singular Cauchy problem of semilinear Euler-Poisson-Darboux equation in R^n with subcritical power type nonlinearity. By introducing an improved test function, we obtain an enhanced lower bound for the functional including the spacetime integral of the nonlinear term with an additional logarithmic growth, which finally yields the blow up result and upper bound of lifespan estimate for the corresponding Cauchy problem with "critical" nonlinear power. And this gives some partial answer to the open problem 1 posed by D'Abbicco (J. Differential Equations 286 (2021), 531-556). |
| title | Blow-up of solutions to the Euler-Poisson-Darbox equation with critical power nonlinearity |
| topic | Analysis of PDEs primary: 35L71, secondary: 35Q05 |
| url | https://arxiv.org/abs/2603.19614 |