The Existence and Uniqueness of Nonstationary Ideal Incompressible Flow in Bounded Domains in R 3

1973 ◽  
Vol 179 ◽  
pp. 167
Author(s):  
H. S. G. Swann
Keyword(s):  
Incompressible Flow ◽  
Existence And Uniqueness ◽  
Bounded Domains ◽  
Nonstationary Ideal

scholarly journals Stochastic Navier-Stokes Equations with Artificial Compressibility in Random Durations

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Hong Yin
Keyword(s):  
Incompressible Flow ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Finite Dimensional

The existence and uniqueness of adapted solutions to the backward stochastic Navier-Stokes equation with artificial compressibility in two-dimensional bounded domains are shown by Minty-Browder monotonicity argument, finite-dimensional projections, and truncations. Continuity of the solutions with respect to terminal conditions is given, and the convergence of the system to an incompressible flow is also established.

scholarly journals Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Imed Bachar ◽  
Habib Mâagli
Keyword(s):  
Dirichlet Problem ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Nonlinear Effects ◽  
Weight Functions ◽  
Global Behavior ◽  
Bounded Domains ◽  
Euclidian Distance ◽  
Nonnegative Weight

We prove the existence and uniqueness of a positive continuous solution to the following singular semilinear fractional Dirichlet problem(-Δ)α/2u=a1(x)uσ1+a2(x)uσ2, in D  limx→z∈∂D(δ(x))1-(α/2)u(x)=0,where0<α<2, σ1,  σ2∈(-1,1), Dis a boundedC1,1-domain inℝn,n≥2,andδ(x)denotes the Euclidian distance fromxto the boundary ofD.The nonnegative weight functionsa1,  a2are required to satisfy certain hypotheses related to the Karamata class. We also investigate the global behavior of such solution.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

scholarly journals Viscosity solutions associated with impulse control problems for piecewise-deterministic processes

1989 ◽  
Vol 12 (1) ◽  
pp. 145-157 ◽  
Author(s):  
Suzanne M. Lenhart
Keyword(s):  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Impulse Control ◽  
Control Problems ◽  
Bounded Domains ◽  
Existence And Uniqueness Results ◽  
Impulse Control Problem ◽  
Uniqueness Results ◽  
Deterministic Processes ◽  
Piecewise Deterministic Processes

This paper considers existence and uniqueness results for viscosity solutions of integro-differential equations associated with the impulse control problem for piecewise-deterministic processes on bounded domains and on Rn.

ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO MAXWELL'S EQUATIONS IN BOUNDED DOMAINS WITH APPLICATION TO MAGNETOTELLURICS

2000 ◽  
Vol 10 (04) ◽  
pp. 615-628 ◽  
Author(s):  
JUAN E. SANTOS ◽  
DONGWOO SHEEN
Keyword(s):  
Existence And Uniqueness ◽  
Electromagnetic Waves ◽  
Regularity Result ◽  
Absorbing Boundary Conditions ◽  
Bounded Domains ◽  
Uniqueness Of Solutions ◽  
Absorbing Boundary ◽  
Lipschitz Continuous ◽  
Time Harmonic ◽  
Electric And Magnetic Fields

We analyze the solution of the time-harmonic Maxwell equations with vanishing electric permittivity in bounded domains and subject to absorbing boundary conditions. The problem arises naturally in magnetotellurics when considering the propagation of electromagnetic waves within the earth's interior. Existence and uniqueness are shown under the assumption that the source functions are square integrable. In this case, the electric and magnetic fields belong to H(curl; Ω). If, in addition, the divergences of the source functions are square integrable and the coefficients are Lipschitz-continuous, a stronger regularity result is obtained. A decomposition of the space of square integrable vector functions and a new compact imbedding result are exploited.

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