scholarly journals On connection between the order of a stationary one-dimensional dispersive equation and the growth of its convective term

2021 ◽  
Vol 39 (3) ◽  
pp. 157-175
Author(s):  
Nikolai Andreevitch Larkin ◽  
Jackson Luchesi
Keyword(s):  
Boundary Value Problem ◽  
Regular Solution ◽  
Continuous Dependence ◽  
Boundary Value ◽  
Critical Values ◽  
Convective Term ◽  
Dispersive Equation ◽  
One Dimensional

A boundary value problem for a stationary nonlinear dispersive equation of 2l+1 order with a convective term in the form u^ku_x, k\in N was considered on an interval (0,L). The existence, uniqueness and continuous dependence  of a regular solution as well as a relation between the order l and critical values of k of the equation have been established.

scholarly journals Higher-Order Stationary Dispersive Equations on Bounded Intervals

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
N. A. Larkin ◽  
J. Luchesi
Keyword(s):  
Boundary Value Problem ◽  
Regular Solution ◽  
Continuous Dependence ◽  
Boundary Value ◽  
Higher Order ◽  
Dispersive Equations ◽  
Dispersive Equation

A boundary value problem for a stationary nonlinear dispersive equation of 2l+1 order on an interval (0,L) was considered. The existence, uniqueness, and continuous dependence of a regular solution have been established.

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

scholarly journals Pairs of nodal solutions for a Minkowski-curvature boundary value problem in a ball

2019 ◽  
Vol 21 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Alberto Boscaggin ◽  
Maurizio Garrione
Keyword(s):  
Boundary Value Problem ◽  
Neumann Problem ◽  
Boundary Value ◽  
Periodic Problem ◽  
Nodal Solutions ◽  
Shooting Technique ◽  
One Dimensional ◽  
Dimensional Equation

By using a shooting technique, we prove that the quasilinear boundary value problem [Formula: see text] where [Formula: see text] is a ball and [Formula: see text], has more and more pairs of nodal solutions on growing of the parameter [Formula: see text]. The radial Neumann problem and the periodic problem for the corresponding one-dimensional equation are considered, as well.

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