Second order quasilinear functional evolution equations

László Simon

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 2, page 139-152
  • ISSN: 0862-7959

Abstract

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We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in ( 0 , T ) is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in ( 0 , ∞ ) (boundedness and stabilization as t → ∞ ) are shown.

How to cite

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Simon, László. "Second order quasilinear functional evolution equations." Mathematica Bohemica 140.2 (2015): 139-152. <http://eudml.org/doc/271584>.

@article{Simon2015,
abstract = {We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in $(0,T)$ is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in $(0,\infty )$ (boundedness and stabilization as $t\rightarrow \infty $) are shown.},
author = {Simon, László},
journal = {Mathematica Bohemica},
keywords = {functional evolution equation; second order quasilinear equation; monotone operator},
language = {eng},
number = {2},
pages = {139-152},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Second order quasilinear functional evolution equations},
url = {http://eudml.org/doc/271584},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Simon, László
TI - Second order quasilinear functional evolution equations
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 2
SP - 139
EP - 152
AB - We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in $(0,T)$ is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in $(0,\infty )$ (boundedness and stabilization as $t\rightarrow \infty $) are shown.
LA - eng
KW - functional evolution equation; second order quasilinear equation; monotone operator
UR - http://eudml.org/doc/271584
ER -

References

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