A mixed problem for quasilinear impulsive hyperbolic equations with non stationary boundary and transmission conditions.
A property of the defining equations for the Lie algebra in the group classification problem for wave equations.
Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent
In this paper, we show finite time blow-up of solutions of the p−wave equation in ℝN, with critical Sobolev exponent. Our work extends a result by Galaktionov and Pohozaev [4]
Exact boundary controllability for quasilinear wave equations in a planar tree-like network of strings
Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms
We consider the existence, both locally and globally in time, the decay and the blow up of the solution for the extensible beam equation with nonlinear damping and source terms. We prove the existence of the solution by Banach contraction mapping principle. The decay estimates of the solution are proved by using Nakao’s inequality. Moreover, under suitable conditions on the initial datum, we prove that the solution blow up in finite time.
Exponential decay of energy for some nonlinear hyperbolic equations with strong dissipation.
Global existence and asymptotic behavior of solutions for some nonlinear hyperbolic equation.
Global existence, uniqueness, and asymptotic behavior of solution for -Laplacian type wave equation.
Global solutions of quasilinear systems of Klein–Gordon equations in 3D
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.
Quasilineare Differentialgleichungen zweiter Ordnung vom hyperbolischen Typus. Gemischte Randwertaufgaben
Stabilité en temps grand pour les petites solutions d’équations de Klein-Gordon quasilinéaires sur
The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region .
Решение задачи Коши для квазилинейных гиперболических уравнений и линейных гиперболических систем методом конечных разностей