Geodesic
Second order quasilinear functional evolution equations
Mathematica Bohemica, Tome 140 (2015) no. 2, pp. 139-152.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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\to \infty $) are shown.
DOI : 10.21136/MB.2015.144322
Classification : 35A01, 35A02, 35B35, 35R10, 35R20
Keywords: functional evolution equation; second order quasilinear equation; monotone operator 
@article{10_21136_MB_2015_144322,
     author = {Simon, L\'aszl\'o},
     title = {Second order quasilinear functional evolution equations},
     journal = {Mathematica Bohemica},
     pages = {139--152},
     publisher = {mathdoc},
     volume = {140},
     number = {2},
     year = {2015},
     doi = {10.21136/MB.2015.144322},
     mrnumber = {3368490},
     zbl = {06486930},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144322/}
}
TY  - JOUR
AU  - Simon, László
TI  - Second order quasilinear functional evolution equations
JO  - Mathematica Bohemica
PY  - 2015
SP  - 139
EP  - 152
VL  - 140
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144322/
DO  - 10.21136/MB.2015.144322
LA  - en
ID  - 10_21136_MB_2015_144322
ER  - 
%0 Journal Article
%A Simon, László
%T Second order quasilinear functional evolution equations
%J Mathematica Bohemica
%D 2015
%P 139-152
%V 140
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144322/
%R 10.21136/MB.2015.144322
%G en
%F 10_21136_MB_2015_144322
Simon, László. Second order quasilinear functional evolution equations. Mathematica Bohemica, Tome 140 (2015) no. 2, pp. 139-152. doi : 10.21136/MB.2015.144322. http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144322/

Cité par Sources :