Non-linear vibration of beams with time-dependent boundary conditions

1973 ◽  
Vol 8 (3) ◽  
pp. 195-212 ◽  
Author(s):  
K.S. Aravamudan ◽  
P.N. Murthy
Keyword(s):  
Boundary Conditions ◽  
Time Dependent ◽  
Linear Vibration ◽  
Non Linear

Wavelet Based Solution to Time-Dependent Higher Order Non-Linear Two-Point Initial Boundary Value Problems With Non-Periodic Boundary Conditions: KdV, Boussinesq Equations

2003 ◽  
Author(s):  
H. N. Narang ◽  
Rajiv K. Nekkanti
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Initial Boundary ◽  
Time Dependent ◽  
Initial Boundary Value Problems ◽  
Non Linear ◽  
Initial Boundary Value

The Wavelet solution for boundary-value problems is relatively new and has been mainly restricted to the solutions in data compression, image processing and recently to the solution of differential equations with periodic boundary conditions. This paper is concerned with the wavelet-based Galerkin’s solution to time dependent higher order non-linear two-point initial-boundary-value problems with non-periodic boundary conditions. The wavelet method can offer several advantages in solving the initial-boundary-value problems than the traditional methods such as Fourier series, Finite Differences and Finite Elements by reducing the computational time near singularities because of its multi-resolution character. In order to demonstrate the wavelet, we extend our prior research of solution to parabolic equations and problems with non-linear boundary conditions to non-linear problems involving KdV Equation and Boussinesq Equation. The results of the wavelet solutions are examined and they are found to compare favorably to the known solution. This paper on the whole indicates that the wavelet technique is a strong contender for solving partial differential equations with non-periodic conditions.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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