Related papers: Exploring Critical Collapse in the Semilinear Wave…
In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schr\"{o}dinger equations, which arises in the interaction between the matter and the electromagnetic field for the semiconductor quantum devices. A…
This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semilinear terms including the space-derivative of the unknown…
The global existence for semilinear wave equations with space-dependent critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are in mind.…
In this paper, we study the initial value problem for semilinear wave equations with the time-dependent and scale-invariant damping in two dimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa in 2019, we obtain the…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
In this work we derive some blow-up results for semilinear wave equations both in de Sitter and anti-de Sitter spacetimes. By requiring suitable conditions on a time-dependent factor in the nonlinear term, we prove the blow-up in finite…
We study the long time existence of solutions to nonlinear wave equations with power-type nonlinearity (of order $p$) and small data, on a large class of $(1+n)$-dimensional nonstationary asymptotically flat backgrounds, which include the…
We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck equations, which are a nonlinear coupled system widely used in semiconductors and ion channels. The spatial…
This paper addresses the properties of Continuous Interior Penalty (CIP) finite element solutions for the Helmholtz equation. The $h$-version of the CIP finite element method with piecewise linear approximation is applied to a…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition…
This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…
We study the dynamics of the critical collapse of a spherically symmetric scalar field. Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained. In the central region, owing to the…
We propose and analyze a space-time finite element method for Westervelt's quasilinear model of ultrasound waves in second-order formulation. The method combines conforming finite element spatial discretizations with a…
We study the critical collapse of a massless scalar field with angular momentum in spherical symmetry. In order to mimic the effects of angular momentum we perform a sum of the stress-energy tensors for all the scalar fields with the same…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
In this paper, we propose and analyse a numerical method to solve 2D Dirichlet time-harmonic elastic wave equations. The procedure is based on the decoupling of the elastic vector field into scalar Pressure ($P$-) and Shear ($S$-) waves via…
The full discretization of the semi-linear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is…
In this paper we study the long time behavior for a semilinear wave equation with space-dependent and nonlinear damping term. After rewriting the equation as a first order system, we define a class of approximate solutions that employ…