Exponential growth of positive initial-energy solutions of a system of...
AbstractThis work is concerned with a system of nonlinear viscoelastic wave equations with nonlinear damping and source terms acting in both equations. We will prove that the energy associated to the...
View ArticleExistence and asymptotic stability of a viscoelastic wave equation with a delay
AbstractIn this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem $$u_{tt}(x,t)-\Delta...
View ArticleGeneral decay of solutions of a nonlinear system of viscoelastic wave equations
AbstractThis work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the...
View ArticleExistence and Asymptotic Behavior of the Wave Equation with Dynamic Boundary...
AbstractThe goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping....
View ArticleDecay Rate of Solutions to Timoshenko System with Past History in Unbounded...
AbstractWe consider the Cauchy problem for the one-dimensional Timoshenko system coupled with the heat conduction, wherein the latter is described by the Gurtin–Pipkin thermal law. We study the decay...
View ArticleOn the Jordan–Moore–Gibson–Thompson Wave Equation in Hereditary Fluids with...
AbstractWe prove global solvability of the third-order in time Jordan–More–Gibson–Thompson acoustic wave equation with memory in \({\mathbb {R}}^n\), where \(n \ge 3\). This wave equation models...
View ArticleOn the Cauchy problem of the standard linear solid model with Fourier heat...
AbstractIn this paper, we consider the standard linear solid model in \(\mathbb {R}^N\) coupled with the Fourier law of heat conduction. First, we give the appropriate functional setting to prove the...
View ArticleGlobal existence for the Jordan–Moore–Gibson–Thompson equation in Besov spaces
AbstractIn this paper, we consider the Cauchy problem of a model in nonlinear acoustic, named the Jordan–Moore–Gibson–Thompson equation. This equation arises as an alternative model to the well-known...
View ArticleStability of the Couette Flow for a 2D Boussinesq System Without Thermal...
AbstractIn this paper, we prove the stability of the Couette flow for a 2D Navier–Stokes Boussinesq system without thermal diffusivity for the initial perturbation in Gevrey-\(\frac{1}{s}\),...
View ArticleTime-weighted estimates for the Blackstock equation in nonlinear ultrasonics
AbstractHigh frequencies at which ultrasonic waves travel give rise to nonlinear phenomena. In thermoviscous fluids, these are captured by Blackstock’s acoustic wave equation with strong damping. We...
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