Geodesic
Blow-Up of the Solution of the Initial Boundary-Value Problem for the Generalized Boussinesq Equation with Nonlinear Boundary Condition
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 567-582

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

The initial boundary-value problem for a nonlinear equation of pseudoparabolic type with nonlinear Neumann boundary condition is considered. We prove a local theorem on the existence of solutions. Using the method of energy inequalities, we obtain sufficient conditions for the blow-up of solutions in a finite time interval and establish upper and lower bounds for the blow-up time.
Mots-clés : Boussinesq equation, pseudoparabolic-type equation
Keywords: initial boundary-value problem, Neumann boundary condition, blow-up of solutions, homogenous isotropic semiconductor, Galerkin's method, dissipative processes in a semiconductor. 
@article{MZM_2012_92_4_a7,
     author = {P. A. Makarov},
     title = {Blow-Up of the {Solution} of the {Initial} {Boundary-Value} {Problem} for the {Generalized} {Boussinesq} {Equation} with {Nonlinear} {Boundary} {Condition}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {567--582},
     publisher = {mathdoc},
     volume = {92},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a7/}
}
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P. A. Makarov. Blow-Up of the Solution of the Initial Boundary-Value Problem for the Generalized Boussinesq Equation with Nonlinear Boundary Condition. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 567-582. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a7/