Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion
| dc.contributor.author | Arumugam, Gurusamy | |
| dc.contributor.author | Erhardt, Andre H. | |
| dc.date.accessioned | 2021-10-11T20:41:29Z | |
| dc.date.available | 2021-10-11T20:41:29Z | |
| dc.date.issued | 2020-12-17 | |
| dc.description.abstract | We establish the existence and uniqueness of weak solutions to the parabolic system with nonstandard growth condition and cross diffusion, ∂tu - div α(x, t, ∇u)) = div |F|p(x,t)-2 F), ∂tv - div α(x, t, ∇v)) = δ∆u, where δ ≥ 0 and ∂tu, ∂tv denote the partial derivative of u and v with respect to the time variable t, while ∇u and ∇v denote the one with respect to the spatial variable x. Moreover, the vector field α(x, t, ‧) satisfies certain nonstandard p(x, t) growth, monotonicity and coercivity conditions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Arumugam, G., & Erhardt, A. H. (2020). Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion. <i>Electronic Journal of Differential Equations, 2020</i>(123), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14633 | |
| 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, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Nonlinear parabolic problem | |
| dc.subject | Nonstandard growth | |
| dc.subject | Cross diffusion | |
| dc.title | Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion | |
| dc.type | Article |