scholarly journals Absolute continuity of the law for solutions of stochastic differential equations with boundary noise

2017 ◽  
Vol 17 (06) ◽  
pp. 1750045
Author(s):  
Stefano Bonaccorsi ◽  
Margherita Zanella
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Stochastic Perturbation ◽  
Neumann Boundary ◽  
Brownian Motion Process ◽  
Motion Process ◽  
Stochastic Term ◽  
The Law ◽  
Boundary Noise ◽  
Smooth Density

We study the existence and regularity of the density for the solution [Formula: see text] (with fixed [Formula: see text] and [Formula: see text]) of the heat equation in a bounded domain [Formula: see text] driven by a stochastic inhomogeneous Neumann boundary condition with stochastic term. The stochastic perturbation is given by a fractional Brownian motion process. Under suitable regularity assumptions on the coefficients, by means of tools from the Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure in [Formula: see text].

Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Agil K. Khanmamedov ◽  
Nigar F. Gafarova
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Inverse Spectral Problem ◽  
Anharmonic Oscillator ◽  
Neumann Boundary ◽  
Effective Algorithm ◽  
Inverse Spectral Problems ◽  
Main Equation ◽  
Inverse Spectral ◽  
Half Axis

AbstractAn anharmonic oscillator {T(q)=-\frac{d^{2}}{dx^{2}}+x^{2}+q(x)} on the half-axis {0\leq x<\infty} with the Neumann boundary condition is considered. By means of transformation operators, the direct and inverse spectral problems are studied. We obtain the main integral equations of the inverse problem and prove that the main equation is uniquely solvable. An effective algorithm for reconstruction of perturbed potential is indicated.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

scholarly journals Pointwise observation of the state given by complex time lag parabolic system

2017 ◽  
Vol 27 (1) ◽  
pp. 77-89
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Optimization Problems ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Time Lags

AbstractVarious optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.

An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition

2018 ◽  
Vol 356 ◽  
pp. 115-126 ◽  
Author(s):  
Yesom Park ◽  
Jeongho Kim ◽  
Jinwook Jung ◽  
Euntaek Lee ◽  
Chohong Min
Keyword(s):  
Boundary Condition ◽  
Poisson Equation ◽  
Neumann Boundary Condition ◽  
Neumann Boundary
Sign in / Sign up

Export Citation Format

Share Document