Existence and uniqueness of the solution of linear degenerate PDEs in weighted Sobolev space with nonhomogeneous boundary condition

2017 ◽  
Author(s):  
Raj Narayan Dhara
Keyword(s):  
Boundary Condition ◽  
Sobolev Space ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Space ◽  
Nonhomogeneous Boundary Condition ◽  
Nonhomogeneous Boundary ◽  
Uniqueness Of The Solution ◽  
Linear Degenerate

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

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 Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Jukka Kemppainen
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Diffusion Equation ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Robin Boundary Condition ◽  
Fractional Diffusion ◽  
Uniqueness Of The Solution ◽  
Time Fractional Diffusion Equation ◽  
Robin Boundary

Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition on a bounded domain with Lyapunov boundary is proved in the space of continuous functions up to boundary. Since a Green matrix of the problem is known, we may seek the solution as the linear combination of the single-layer potential, the volume potential, and the Poisson integral. Then the original problem may be reduced to a Volterra integral equation of the second kind associated with a compact operator. Classical analysis may be employed to show that the corresponding integral equation has a unique solution if the boundary data is continuous, the initial data is continuously differentiable, and the source term is Hölder continuous in the spatial variable. This in turn proves that the original problem has a unique solution.

scholarly journals The Cauchy Problem for Parabolic Equations with Degeneration

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Ivan Pukal’skii ◽  
Bohdan Yashan
Keyword(s):  
Boundary Condition ◽  
Cauchy Problem ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Arbitrary Order ◽  
Power Weight ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Set Of Points

Annotation. For a second-order parabolic equation, the multipoint in time Cauchy problem is considered. The coefficients of the equation and the boundary condition have power singularities of arbitrary order in time and space variables on a certain set of points. Conditions for the existence and uniqueness of the solution of the problem in Hölder spaces with power weight are found.

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