Parabolic Equations in ℝ d + with More General Boundary Conditions

2021 ◽  
pp. 199-228
Author(s):  
Luca Lorenzi ◽  
Abdelaziz Rhandi
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
General Boundary ◽  
General Boundary Conditions

scholarly journals Higher-Order Parabolic Equations with VMO Assumptions and General Boundary Conditions with Variable Leading Coefficients

2018 ◽  
Vol 2020 (7) ◽  
pp. 2114-2144 ◽  
Author(s):  
Hongjie Dong ◽  
Chiara Gallarati
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Parabolic Equations ◽  
Higher Order ◽  
Elliptic Operators ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Elliptic And Parabolic Equations ◽  
Boundary Operators ◽  
Higher Order Parabolic Equations

Abstract We prove weighted mixed $L_{p}(L_{q})$-estimates, with $p,q\in (1,\infty )$, and the corresponding solvability results for higher-order elliptic and parabolic equations on the half space ${\mathbb{R}}^{d+1}_{+}$ and on general $C^{2m-1,1}$ domains with general boundary conditions, which satisfy the Lopatinskii–Shapiro condition. We assume that the elliptic operators A have leading coefficients that are in the class of vanishing mean oscillations both in the time and the space variables and that the boundary operators have variable leading coefficients. The proofs are based on and generalize the estimates recently obtained by the authors in [6].

Flexural Vibration Response of Beams With General Boundary Conditions: A Transfer Matrix Approach

1991 ◽  
Author(s):  
T. Önsay
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Response ◽  
General Boundary ◽  
Phase Variable ◽  
General Boundary Conditions ◽  
Transfer Matrices ◽  
Analytical Results

Abstract The wave-mode representation is utilized to obtain a more efficient form to the conventional transfer matrix method for bending vibrations of beams. The proposed improvement is based on a phase-variable canonical state representation of the equation governing the time-harmonic flexural vibrations of a beam. Transfer matrices are obtained for external forces, step-change of beam properties, intermediate supports and for boundaries. The transfer matrices are utilized to obtain the vibration response of a point-excited single-span beam with general boundary conditions. The general characteristic equation and the transfer mobility of a single-span beam are determined. The application of the analytical results are demonstrated on physical structures with different boundary conditions. A hybrid model is developed to incorporate measured impedance of nonideal boundaries into the transfer matrix method. The analytical results are found to be in excellent agreement with experimental measurements.

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