Nonexistence results for hyperbolic type inequalities involving the Grushin operator in exterior domains
| dc.contributor.author | Jleli, Mohamed | |
| dc.contributor.author | Samet, Bessem | |
| dc.date.accessioned | 2022-10-25T17:10:08Z | |
| dc.date.available | 2022-10-25T17:10:08Z | |
| dc.date.issued | 2021-09-14 | |
| dc.description.abstract | We study the hyperbolic type differential inequality utt(t, x, y) - Lℓu(t, x, y) ≥ |u(t, x, y)|p, (t, x, y) ∈ (0, ∞) x D1 x D2 under the boundary conditions u(t, x, y) ≥ ƒ(x), (t, x, y) ∈ (0, ∞) x ∂D1 x D2 u(t, x, y) ≥ g(y), (t, x, y) ∈ (0, ∞) x D1 x ∂D2 where p > 1, Dk = {z ∈ ℝNk : |z| ≥ 1}, K = 1, 2, Nk ≥ 2, ƒ ∈ L1(∂D1), g ∈ L1 (∂D2), and Lℓ, ℓ ∈ ℝ, is the Grushin operator Lℓu = ∆xu + |x|2ℓ ∆yu. We obtain sufficient conditions depending on p, ℓ, N1 = N2 = 2; N1 = 2, N2 ≥ 3; N1 ≥ 3, N2 = 2; N1, N1, N2 ≥ 3. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 26 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Jleli, M., & Samet, B. (2021). Nonexistence results for hyperbolic type inequalities involving the Grushin operator in exterior domains. <i>Electronic Journal of Differential Equations, 2021</i>(75), pp. 1-26. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16233 | |
| 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, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Global weak solutions | |
| dc.subject | Hyperbolic type inequalities | |
| dc.subject | Exterior domain | |
| dc.subject | Grushin operator | |
| dc.title | Nonexistence results for hyperbolic type inequalities involving the Grushin operator in exterior domains | |
| dc.type | Article |