Vector-valued Heat Equations and Networks with Coupled Dynamic Boundary Conditions
نویسنده
چکیده
Motivated by diffusion processes on metric graphs and ramified spaces, we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class. Beside well-posedness, we discuss positivity, L∞-contractivity and further invariance properties. We show that the parabolic problem with dynamic boundary conditions enjoy these properties if and only if so does its counterpart with time-independent boundary conditions. Furthermore, we prove continuous dependence of the solution to the parabolic problem on the boundary conditions in the considered class.
منابع مشابه
Vector-valued Heat Equations with Coupled, Dynamic Boundary Conditions
Abstract. Motivated by diffusion processes on metric graphs and open books, we consider an abstract setting for interface problems with quite general coupled boundary conditions, which we also allow to depend on time. Beside well-posedness, we discuss positivity, L∞-contractivity and further invariance properties. We show that the parabolic problem with time-dependent boundary conditions enjoy ...
متن کاملSome Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations
Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. ...
متن کاملAn Exact Solution for Classic Coupled Magneto-Thermo-Elasticity in Cylindrical Coordinates
In this paper, the classic coupled Magneto-thermo-elasticity model of hollow and solid cylinders under radial-symmetric loading condition (r, t) is considered. A full analytical and the direct method based on Fourier Hankel series and Laplace transform is used, and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body fo...
متن کاملA Coupled Rigid-viscoplastic Numerical Modeling for Evaluating Effects of Shoulder Geometry on Friction Stir-welded Aluminum Alloys
Shoulder geometry of tool plays an important role in friction-stir welding because it controls thermal interactions and heat generation. This work is proposed and developed a coupled rigid-viscoplastic numerical modeling based on computational fluid dynamics and finite element calculations aiming to understand these interactions. Model solves mass conservation, momentum, and energy equations in...
متن کاملNumerical Study of Coupled Fluid Flow and Heat Transfer in a Rectangular Domain at Moderate Reynolds Numbers using the Control Volume Method
In this paper, we have used a control volume method to investigate the problem of a fully coupled fluid flow with heat transfer in a rectangular domain with slip wall boundary conditions. We have used this method to solve the governing equations and thereby to compute the convective and diffusive fluxes at the cell faces of the control volumes considered around the grid points of computational ...
متن کامل