Resonance for Quasilinear Hyperbolic Equation

Global attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$

We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions  $ u(x,0) = u_0 (x)$  and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ;  f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...

Global existence‎, ‎stability results and compact invariant sets‎ ‎for a quasilinear nonlocal wave equation on $mathbb{R}^{N}$

We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $L^{N/2}(mathb...

Rothe Time-discretization Method Applied to a Quasilinear Wave Equation Subject to Integral Conditions

Recently, the study of initial-boundary value problems for hyperbolic equations with boundary integral conditions has received considerable attention. This kind of conditions has many important applications. For instance, they appear in the case where a direct measurement quantity is impossible; however, their mean values are known. In this paper, we deal with a class of quasilinear hyperbolic ...

Mathematical Analysis of some Hyperbolic-Parabolic Inner Obstacle Problems

We establish the existence and uniqueness of the solution to some inner obstacle problems for a coupling of a multidimensional quasilinear firstorder hyperbolic equation set in a region Ωh with a quasilinear parabolic one set in the complementary Ωp = Ω\Ωh. We start by providing the definition of a weak solution through an entropy inequality on the whole domain. Since the interface ∂Ωp ∩ ∂Ωh co...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption