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dc.contributor.authorAntontsev, Stanislav ( Orcid Icon 0000-0002-9469-9902 )
dc.contributor.authorShmarev, Sergey ( Orcid Icon 0000-0002-1783-5165 )
dc.contributor.authorSimsen, Jacson ( Orcid Icon 0000-0002-6683-1363 )
dc.contributor.authorMariza Stefanello, Simsen ( Orcid Icon 0000-0002-2378-2442 )
dc.date.accessioned2021-10-20T14:58:30Z
dc.date.available2021-10-20T14:58:30Z
dc.date.issued2019-02-13
dc.identifier.citationAntontsev, S., Shmarev, S., Simsen, J., & Stefanello Simsen, M. (2019). Differential inclusion for the evolution p(x)-Laplacian with memory. Electronic Journal of Differential Equations, 2019(26), pp. 1-28.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14679
dc.description.abstractWe consider the evolution differential inclusion for a nonlocal operator that involves p(x)-Laplacian, ut - ∆p(x)u - ∫t0 g(t - s) ∆p(x) u(x, s)ds ∈ F(u) in QT = Ω x (0, T), where Ω ⊂ ℝn, n ≥ 1, is a bounded domain with Lipschitz-continuous boundary. The exponent p(x) is a given measurable function, p⎺ ≤ p(x) ≤ p+ a.e. in Ω for some bounded constants p⎺ > max {1, 2n/n+2} and p+ < ∞. It is assumed that g, g′ ∈ L2(0, T), and that the multivalued function F(∙) is globally Lipschitz, has convex closed values and F(0) ≠ ∅. We prove that the homogeneous Dirichlet problem has a local in time weak solution. Also we show that when p⎺ > 2 and uF(u) ⊆ {v ∈ L2(Ω) : v ≤ εu2 a.e. in Ω} with a sufficiently small ε > 0 the weak solution possesses the property of finite speed of propagation of disturbances from the initial data and may exhibit the waiting time property. Estimates on the evolution of the null-set of the solution are presented.
dc.formatText
dc.format.extent28 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectEvolution p(x)-Laplacianen_US
dc.subjectNonlocal equationen_US
dc.subjectDifferential inclusionen_US
dc.subjectFinite speed of propagationen_US
dc.subjectWaiting timeen_US
dc.titleDifferential inclusion for the evolution p(x)-Laplacian with memoryen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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