Instability of an Equilibrium of a Partial Differential Equation
نویسنده
چکیده
A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the equilibrium is not stable.
منابع مشابه
Exact Analytical Solution for Bending Analysis of Functionally Graded Annular Sector Plates
In this article, an exact levy solution is presented for bending analysis of a functionally graded (FG) annular sector plate. The governing equilibrium equations are obtained based on the classical plate theory. Introducing an analytical method for the first time, the three coupled governing equilibrium equations are replaced by an independent equation in term of transverse deflection. This equ...
متن کاملA Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...
متن کاملAn analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients. At first, the non-self-adjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence ...
متن کاملAPPLICATION OF PARTIAL DIFFERENTIAL EQUATIONS IN SNOW MECHANICS
In the present work, failure of a snow slab is analyzed by accounting Normal mode criteria. The analysis has been extended to include residual stress into the model (in addition to body forces). Intensity of crack energy release rate, and displacement components have been derived and their values have been estimated. The obtained results have been compared with the existing snow slab failure mo...
متن کاملSpectrally formulated finite element for vibration analysis of an Euler-Bernoulli beam on Pasternak foundation
In this article, vibration analysis of an Euler-Bernoulli beam resting on a Pasternak-type foundation is studied. The governing equation is solved by using a spectral finite element model (SFEM). The solution involves calculating wave and time responses of the beam. The Fast Fourier Transform function is used for temporal discretization of the governing partial differential equation into a se...
متن کامل