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dc.contributor.authorNualart, Marc ( Orcid Icon 0000-0003-3697-3421 )
dc.date.accessioned2021-10-13T14:05:50Z
dc.date.available2021-10-13T14:05:50Z
dc.date.issued2020-12-26
dc.identifier.citationNualart, M. (2020). Distributional solutions for damped wave equations. Electronic Journal of Differential Equations, 2020(131), pp. 1-16.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14642
dc.description.abstractThis work presents results on solutions to the one-dimensional damped wave equation, also called telegrapher's equation, when the initial conditions are general distributions. We make a complete deduction of its fundamental solutions, both for positive and negative times. To obtain them we only use self-similarity arguments and distributional calculus, making no use of Fourier or Laplace transforms. We next use these fundamental solutions to prove both the existence and the uniqueness of solutions to the distributional initial value problem. As applications we recover the semi-group property for initial data in classical function spaces, and we find the probability distribution function for a recent financial model of evolution of prices.en_US
dc.formatText
dc.format.extent16 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectPartial differential equationsen_US
dc.subjectDamped wave equationen_US
dc.subjectDistributional solutionen_US
dc.subjectInitial value problemen_US
dc.titleDistributional solutions for damped wave equationsen_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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