Geodesic
On the Absence of Local Solutions of Several Evolutionary Problems
Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 337-349

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

We consider the existence problem for local (with respect to time) solutions of quasilinear evolutionary partial differential equations and inequalities with singular coefficients and initial conditions. We obtain sufficient conditions for instantaneous blow-up of solutions and show that the results thus obtained cannot be improved in the function class under study.
Keywords: existence problem, quasilinear evolutionary PDE, weak solution, Dirichlet boundary condition, heat equation, Sobolev space, Carathéodory function. 
@article{MZM_2009_86_3_a2,
     author = {E. I. Galakhov},
     title = {On the {Absence} of {Local} {Solutions} of {Several} {Evolutionary} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {337--349},
     publisher = {mathdoc},
     volume = {86},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a2/}
}
TY  - JOUR
AU  - E. I. Galakhov
TI  - On the Absence of Local Solutions of Several Evolutionary Problems
JO  - Matematičeskie zametki
PY  - 2009
SP  - 337
EP  - 349
VL  - 86
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a2/
LA  - ru
ID  - MZM_2009_86_3_a2
ER  - 
%0 Journal Article
%A E. I. Galakhov
%T On the Absence of Local Solutions of Several Evolutionary Problems
%J Matematičeskie zametki
%D 2009
%P 337-349
%V 86
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a2/
%G ru
%F MZM_2009_86_3_a2
E. I. Galakhov. On the Absence of Local Solutions of Several Evolutionary Problems. Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 337-349. http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a2/