Instantaneous blow-up of semilinear non-autonomous equations with fractional diffusion
| dc.contributor.author | Villa-Morales, Jose | |
| dc.date.accessioned | 2022-04-13T20:13:46Z | |
| dc.date.available | 2022-04-13T20:13:46Z | |
| dc.date.issued | 2017-05-02 | |
| dc.description.abstract | We consider the Cauchy initial value problem ∂/∂t u (t, x) = k(t)∆α u (t, x) + h(t)ƒ(u(t, x)), u(0, x) = u0(x), where ∆α is the fractional Laplacian for 0 < α ≤ 2. We prove that if the initial condition u0 is non-negative, bounded and measurable then the problem has a global integral solution when the source term ƒ is non-negative, locally Lipschitz and satisfies the generalized Osgood's condition ∫∞∥u0∥∞ ds/ƒ(s) ≥ ∫∞0 h(s)ds. Also, we prove that if the initial data is unbounded then the generalized Osgood's condition does not guarantee the existence of a global solution. It is important to point out that the proof of the existence hinges on the role of the function h. Analogously, the function k plays a central role in the proof of the instantaneous blow-up. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Villa-Morales, J. (2017). Instantaneous blow-up of semilinear non-autonomous equations with fractional diffusion. <i>Electronic Journal of Differential Equations, 2017</i>(116), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15650 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Generalized Osgood's condition | |
| dc.subject | Semilinear equations | |
| dc.subject | Fractional diffusion | |
| dc.subject | Instantaneous blow-up | |
| dc.title | Instantaneous blow-up of semilinear non-autonomous equations with fractional diffusion | |
| dc.type | Article |