scholarly journals Singular and Degenerate Boundary Value Problems Related to the Electricity Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Maria-Magdalena Boureanu ◽  
Andaluzia Matei
Keyword(s):  
Sobolev Space ◽  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Weighted Sobolev Space ◽  
Nonlinear Boundary Conditions ◽  
Uniqueness Result ◽  
Physical Phenomena ◽  
Mathematical Literature ◽  
Weak Solvability

The present paper draws attention to the weak solvability of a class of singular and degenerate problems with nonlinear boundary conditions. These problems derive from the electricity theory serving as mathematical models for physical phenomena related to the anisotropic media with “perfect” insulators or “perfect” conductors points. By introducing an appropriate weighted Sobolev space to the mathematical literature, we establish an existence and uniqueness result.

scholarly journals TWO INITIAL-BOUNDARY VALUE PROBLEMS WITH NONLINEAL BOUNDARY CONDITIONS FOR ONE-DIMENSION HYPERBOLIC EQUATION

2017 ◽  
Vol 17 (2) ◽  
pp. 46-56
Author(s):  
L.S. Pulkina ◽  
M.V. Strigun
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Nonlinear Boundary Conditions ◽  
One Dimension ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

In this paper, the initial-boundary value problems for hyperbolic equationwith nonlinear boundary conditions are considered. Existence and uniqueness ofgeneralized solution are proved.

Existence and uniqueness for two-point boundary value problems

1981 ◽  
Vol 88 (3-4) ◽  
pp. 219-234 ◽  
Author(s):  
John V. Baxley ◽  
Sarah E. Brown
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Point Boundary ◽  
Initial Value

SynopsisBoundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

scholarly journals On a Nonlinear Degenerate Evolution Equation with Nonlinear Boundary Damping

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
A. T. Lourêdo ◽  
G. Siracusa ◽  
C. A. Silva Filho
Keyword(s):  
Evolution Equation ◽  
Global Stability ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Boundary Damping ◽  
Degenerate Evolution Equation ◽  
Neumann Type ◽  
Nonlinear Degenerate

This paper deals essentially with a nonlinear degenerate evolution equation of the formKu″-Δu+∑j=1nbj∂u′/∂xj+uσu=0supplemented with nonlinear boundary conditions of Neumann type given by∂u/∂ν+h·, u′=0. Under suitable conditions the existence and uniqueness of solutions are shown and that the boundary damping produces a uniform global stability of the corresponding solutions.

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