English
Related papers

Related papers: Exact boundary observability for nonautonomous qua…

200 papers

We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…

General Relativity and Quantum Cosmology · Physics 2009-06-23 H. -O. Kreiss , O. Reula , O. Sarbach , J. Winicour

This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…

Mathematical Physics · Physics 2012-06-14 Peter C. Gibson

We devise a lucid and straightforward way for explicitly constructing quasi-periodic wave solutions (also called multi-periodic wave solutions) of supersymmetric equations in superspace $\mathbb{R}_\Lambda^{2,1}$ over two-dimensional…

Exactly Solvable and Integrable Systems · Physics 2010-01-12 Engui Fan

In this paper we obtain uniformly locally $L^{\infty}$-estimate of solutions to non-autonomous quasilinear system involving operators in divergence form and a family of nonlinearities that are allowed to grow also critically.

Analysis of PDEs · Mathematics 2026-01-26 Natalino Borgia , Silvia Cingolani , Giuseppina Vannella

In this paper we prove global existence for certain multispeed Dirichlet-wave equations with quadratic nonlinearities outside of obstacles. We assume the natural null condition for systems of quasilinear wave equations with multiple speeds.…

Analysis of PDEs · Mathematics 2007-05-23 Jason Metcalfe , Makoto Nakamura , Christopher D. Sogge

In this paper, we prove the first asymptotic completeness result for a scalar quasilinear wave equation satisfying the weak null condition. The main tool we use in the study of this equation is the geometric reduced system introduced in…

Analysis of PDEs · Mathematics 2024-07-29 Dongxiao Yu

We study generic waves without rotational symmetry in (2+1) - dimensional noncommutative scalar field theory. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by…

High Energy Physics - Theory · Physics 2015-06-12 C. S. Acatrinei

This article concerns the time growth of Sobolev norms of classical solutions to the 3D quasi-linear wave equations with the null condition.

Analysis of PDEs · Mathematics 2015-10-13 Fan Wang

In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…

Optimization and Control · Mathematics 2018-10-03 Xu Liu , Qi Lü , Xu Zhang

The exact distributed controllability of the semilinear wave equation $y_{tt}-y_{xx} + g(y)=f \,1_{\omega}$, assuming that $g$ satisfies the growth condition $\vert g(s)\vert /(\vert s\vert \log^{2}(\vert s\vert))\rightarrow 0$ as $\vert…

Analysis of PDEs · Mathematics 2020-10-28 Arnaud Münch , Emmanuel Trélat

This paper is concerned with locally damped semilinear wave equations defined on compact Riemannian manifolds with boundary. We present a construction of measure-controlled damping regions which are sharp in the sense that their summed…

Analysis of PDEs · Mathematics 2019-08-15 M. M. Cavalcanti , T. F. Ma , P. Marín-Rubio , P. N. Seminario-Huertas

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…

Analysis of PDEs · Mathematics 2026-05-28 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

Numerically computed with high accuracy are periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow of an incompressible inviscid fluid, under gravity, without the effects of surface…

Fluid Dynamics · Physics 2023-01-25 Sergey A. Dyachenko , Vera Mikyoung Hur , Denis A. Silantyev

Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…

Fluid Dynamics · Physics 2009-11-10 V. P. Ruban

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type estimates.

General Relativity and Quantum Cosmology · Physics 2007-05-23 P. Blue , A. Soffer

In this paper we are interested in the behavior of the solutions of non-autonomous damped wave equations when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter…

Analysis of PDEs · Mathematics 2018-08-20 Flank D. M. Bezerra , Gleiciane da Silva Aragão

We study the initial-boundary value problem of quasilinear wave equations outside of a star-shaped obstacle in four space dimensions, in which the nonlinear term under consideration may explicitly depend on the unknown function itself. By…

Analysis of PDEs · Mathematics 2015-03-10 Dongbing Zha , Yi Zhou

This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…

Analysis of PDEs · Mathematics 2022-08-31 Nicolas Vanspranghe , Francesco Ferrante , Christophe Prieur

We consider a Boussinesq system describing one-dimensional internal waves which develop at the boundary between two immiscible fluids, and we restrict to its traveling waves. The method which yields explicitly all the elliptic or degenerate…

Pattern Formation and Solitons · Physics 2017-10-18 Hai Yen Nguyen , Fre'de'ric Dias , Robert Conte

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher…

Analysis of PDEs · Mathematics 2015-05-14 Sijue Wu