Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms

Erhan Pişkin

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page Article ID 127, 14 p., electronic only-Article ID 127, 14 p., electronic only
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Erhan Pişkin. "Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms." Open Mathematics 13.1 (2015): Article ID 127, 14 p., electronic only-Article ID 127, 14 p., electronic only. <http://eudml.org/doc/270857>.

@article{ErhanPişkin2015,
abstract = {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.},
author = {Erhan Pişkin},
journal = {Open Mathematics},
keywords = {Extensible beam equation; Existence; Decay; Blow up; decay; blow up; quasilinear hyperbolic equation; nonlinear damping and source terms; decay estimates of the energy function; Nakao's inequality; lifespan estimates},
language = {eng},
number = {1},
pages = {Article ID 127, 14 p., electronic only-Article ID 127, 14 p., electronic only},
title = {Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms},
url = {http://eudml.org/doc/270857},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Erhan Pişkin
TI - Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - Article ID 127, 14 p., electronic only
EP - Article ID 127, 14 p., electronic only
AB - 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.
LA - eng
KW - Extensible beam equation; Existence; Decay; Blow up; decay; blow up; quasilinear hyperbolic equation; nonlinear damping and source terms; decay estimates of the energy function; Nakao's inequality; lifespan estimates
UR - http://eudml.org/doc/270857
ER -

References

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