Life span of nonnegative solutions to certain quasilinear parabolic Cauchy problems
| dc.contributor.author | Kuiper, Hendrik J. | |
| dc.date.accessioned | 2020-11-25T17:48:51Z | |
| dc.date.available | 2020-11-25T17:48:51Z | |
| dc.date.issued | 2003-06-13 | |
| dc.description.abstract | We consider the problem ρ(x)ut - ∆um = h(x, t)u1+p, x ∈ ℝN, t > 0, with nonnegative, nontrivial, continuous initial condition, u(x, 0) = u0(x) ≢ 0, u0(x) ≥ 0, x ∈ ℝN. An integral inequality is obtained that can be used to find an exponent pc such that this problem has no nontrivial global solution when p ≤ p c. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 ≤ t < T. This is illustrated for the case ρ ≡ 1 and h ≡ 1 with initial condition u(x, 0) = σu0(x), σ > 0, by obtaining a bound of the form T ≤ C0σ-ϧ. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 11 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Kuiper, H. J. (2003). Life span of nonnegative solutions to certain quasilinear parabolic Cauchy problems. <i>Electronic Journal of Differential Equations, 2003</i>(66), pp. 1-11. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13006 | |
| dc.language.iso | en | |
| dc.publisher | Southwest 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, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Nonlinear parabolic equation | |
| dc.subject | Blow-up | |
| dc.subject | Lifespan | |
| dc.subject | Critical exponent | |
| dc.title | Life span of nonnegative solutions to certain quasilinear parabolic Cauchy problems | |
| dc.type | Article |