Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Energetic type estimates for singular hyperbolic equations of high order. (English)
Authors: Musteata A. T.
Abstract
We study the equation $Pu+\lambda Qu=f(t,x,\lambda)$, $t>0$, $x\in R^1$, where $P$ and $Q$ are strictly hyperbolic operators whit variables coefficients of order $n$ and $n-1$ and $\lambda$ is a real parameter. We prove that if $P$ and $Q$ form a strictly hyperbolic pair then the solutions of this equation can be $a$ priori estimated uniform in $\lambda$.Institutul de Matematică Academia de Ştiinţe
str. Academiei 5, MD-2028 Chişinău, Moldova
str. Academiei 5, MD-2028 Chişinău, Moldova
Contents
- Topological classification of quadratic systems with a unique finite second order singularity with two zero eigenvalues. (English)
- Lyapunov stability and attraction of rest points of dynamical systems. (Russian)
- Connectedness of the Levinson center of a compact dissipative dynamical system without uniqueness. (Russian)
- Analytic continuation with respect to a parameter in the neighbourhood of zero of Green's function of basic external boundary value problems for the Helmholtz equation. (Russian)
- On absence of eigenvalues of singular, not selfadjoint differential operators. (Russian)
- Affine-invariant conditions for determining the number and multiplicity of singular points of quadratic differential systems. (English)
- Analysis of the condition ${\germ A}(k)$ for four-dimensional systems of differential equations. (Russian)
- Existence of limiting boundary and initial values of weak solutions of parabolic equation. (Russian)
- $L\sb 2$-estimates of solutions of the singular hyperbolic equations. (English)
- Energetic type estimates for singular hyperbolic equations of high order. (English)
- On sufficient conditions of the center for a cubic system of differential equations. (Russian)
- Concordant solutions of multidimensional differential equations. (English)
- Linear particular integrals and the problem of the center. (Russian)
- On algebraic differential equations with an integrating factor of Darboux type. (Russian)
