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.

OBSTACLE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS WITH NONHOMOGENEOUS NONLINEAR BOUNDARY CONDITIONS

2008 ◽  
Vol 18 (11) ◽  
pp. 1869-1893 ◽  
Author(s):  
FUENSANTA ANDREU ◽  
NOUREDDINE IGBIDA ◽  
JOSÉ M. MAZÓN ◽  
JULIÁN TOLEDO
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Maximal Monotone ◽  
Nonlinear Boundary Conditions ◽  
Obstacle Problems ◽  
Laplacian Operator ◽  
Usual Sense ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic

In this paper we study the questions of existence and uniqueness of solutions for equations of type - div a(x,Du) + γ(u) ∋ ϕ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x,Du) · η + β(u) ∋ ψ. The nonlinear elliptic operator div a(x,Du) modeled on the p-Laplacian operator Δp(u) = div (|Du|p-2Du), with p > 1, γ and β maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) ∩ β(0), [Formula: see text] and the data ϕ ∈ L1(Ω) and ψ ∈ L1(∂ Ω). Since D(γ) ≠ ℝ, we are dealing with obstacle problems. For this kind of problems the existence of weak solution, in the usual sense, fails to be true for nonhomogeneous boundary conditions, so a new concept of solution has to be introduced.

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.

Elliptic-Parabolic Equation with Absorption of Obstacle type

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Noureddine Igbida ◽  
Fahd Karami
Keyword(s):  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Uniqueness Of Solutions ◽  
Degenerate Parabolic Problem ◽  
Doubly Nonlinear ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

AbstractThis paper is concerned with existence and uniqueness of solutions for a doubly nonlinear degenerate parabolic problem of the type β(w)

scholarly journals Existence and uniqueness theorems for some fourth-order nonlinear boundary value problems

2000 ◽  
Vol 23 (11) ◽  
pp. 783-788 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Uniqueness Theorems ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of Solutions ◽  
Order Ordinary Differential Equation ◽  
Carathéodory Conditions

Let G and f:[0,1]×ℝ4→ℝ be two functions satisfying Caratheodory conditions. This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y′′′′+λy′′+ky+G(x,y,y′,y′′,y′′′)=f(x,y,y′,y′′,y′′′) with one of a particular set of boundary conditions.

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