Geodesic
On the Blow-Up of the Solution of an Equation Related to the Hamilton--Jacobi Equation
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 81-95

Voir la notice de l'article provenant de la source Math-Net.Ru

A new model three-dimensional third-order equation of Hamilton–Jacobi type is derived. For this equation, the initial boundary-value problem in a bounded domain with smooth boundary is studied and local solvability in the strong generalized sense is proved; in addition, sufficient conditions for the blow-up in finite time and sufficient conditions for global (in time) solvability are obtained.
Keywords: third-order equation of Hamilton–Jacobi type, blow-up of solutions, electric potential in a crystalline semiconductor, Dirichlet problem, Galerkin approximation, Browder–Minty theorem, Lipschitz-continuous operator. 
@article{MZM_2013_93_1_a7,
     author = {M. O. Korpusov},
     title = {On the {Blow-Up} of the {Solution} of an {Equation} {Related} to the {Hamilton--Jacobi} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {81--95},
     publisher = {mathdoc},
     volume = {93},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a7/}
}
TY  - JOUR
AU  - M. O. Korpusov
TI  - On the Blow-Up of the Solution of an Equation Related to the Hamilton--Jacobi Equation
JO  - Matematičeskie zametki
PY  - 2013
SP  - 81
EP  - 95
VL  - 93
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a7/
LA  - ru
ID  - MZM_2013_93_1_a7
ER  - 
%0 Journal Article
%A M. O. Korpusov
%T On the Blow-Up of the Solution of an Equation Related to the Hamilton--Jacobi Equation
%J Matematičeskie zametki
%D 2013
%P 81-95
%V 93
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a7/
%G ru
%F MZM_2013_93_1_a7
M. O. Korpusov. On the Blow-Up of the Solution of an Equation Related to the Hamilton--Jacobi Equation. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a7/