Geodesic
On the Initial Boundary-Value Problem for a Nonlinear Sobolev-Type Equation with Variable Coefficient
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 643-653

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We study the initial boundary-value problem for a nonlinear Sobolev-type equation with variable coefficient. We obtain sufficient conditions for both global and local (in time) solvability. In the case of local (but not global) solvability, we obtain upper and lower bounds for the existence time of the solution in the form of explicit and quadrature formulas.
Keywords: nonlinear Sobolev-type equation, initial boundary-value problem, Hölder's inequality, blow-up of a solution.
Mots-clés : existence time of a solution, Boussinesq equation 
@article{MZM_2012_91_5_a0,
     author = {A. I. Aristov},
     title = {On the {Initial} {Boundary-Value} {Problem} for a {Nonlinear} {Sobolev-Type} {Equation} with {Variable} {Coefficient}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--653},
     publisher = {mathdoc},
     volume = {91},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a0/}
}
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A. I. Aristov. On the Initial Boundary-Value Problem for a Nonlinear Sobolev-Type Equation with Variable Coefficient. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 643-653. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a0/