Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms
Erhan Pişkin
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library
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We consider the existence, both locally and globally in time, the decay and the blow up of the solution for the extensible beam equation with nonlinear damping and source terms. We prove the existence of the solution by Banach contraction mapping principle. The decay estimates of the solution are proved by using Nakao’s inequality. Moreover, under suitable conditions on the initial datum, we prove that the solution blow up in finite time.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:270857 
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     author = {Erhan Pi\c skin},
     title = {Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms},
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     zbl = {1338.35055},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0040}
}

Erhan Pişkin. Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0040/

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