Persistent regional null controllability of some degenerate wave equations
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DOI: 10.1002/mma.4431
Abstract: This paper is addressed to a study of the persistent regional null controllability problems for one-dimensional linear degenerate wave equations through a distributed controller. Different from non-degenerate wave equations, the classical null controllability results do… read more here.
Keywords: regional null; degenerate; null controllability; degenerate wave ... See more keywords
Exact controllability for some degenerate wave equations
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DOI: 10.1002/mma.6464
Abstract: In this paper, we study one‐dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation… read more here.
Keywords: degenerate; controllability degenerate; wave equations; exact controllability ... See more keywords
Decay rates for semilinear wave equations with vanishing damping and Neumann boundary conditions
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DOI: 10.1002/mma.6733
Abstract: The paper is concerned with the semilinear wave equations with time‐dependent damping γ(t)=α/(1+t) (α>0), under the effect of nonlinear source f behaving like a polynomial, and subject to Neumann boundary conditions. Constructing appropriate auxiliary functions,… read more here.
Keywords: semilinear wave; rates semilinear; boundary conditions; neumann boundary ... See more keywords
Hopf Bifurcation for General 1D Semilinear Wave Equations with Delay
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DOI: 10.1007/s10884-021-10009-1
Abstract: We consider boundary value problems for 1D autonomous damped and delayed semilinear wave equations of the type $$\begin{aligned} \partial ^2_tu(t,x)- a(x,\lambda )^2\partial _x^2u(t,x)= b(x,\lambda ,u(t,x),u(t-\tau ,x),\partial _tu(t,x),\partial _xu(t,x)), \; x \in (0,1) \end{aligned}$$ ∂ t… read more here.
Keywords: general semilinear; hopf bifurcation; bifurcation general; semilinear wave ... See more keywords
Linearly Implicit and High-Order Energy-Conserving Schemes for Nonlinear Wave Equations
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DOI: 10.1007/s10915-020-01245-6
Abstract: A key issue in developing efficient numerical schemes for nonlinear wave equations is the energy-conserving. Most existing schemes of the energy-conserving are fully implicit and the schemes require an extra iteration at each time step… read more here.
Keywords: energy; energy conserving; high order; wave equations ... See more keywords
Pointwise decay for semilinear wave equations on Kerr spacetimes
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DOI: 10.1007/s11005-021-01495-x
Abstract: In this article, we prove pointwise bounds for solutions to the semilinear wave equation with integer powers $$p\ge 3$$ p ≥ 3 on Kerr backgrounds with small angular momentum and small initial data. We expect… read more here.
Keywords: semilinear wave; equations kerr; kerr spacetimes; decay semilinear ... See more keywords
Seismic wave equations in tight oil/gas sandstone media
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DOI: 10.1007/s11430-020-9686-0
Abstract: Tight oil/gas medium is a special porous medium, which plays a significant role in oil and gas exploration. This paper is devoted to the derivation of wave equations in such a media, which take a… read more here.
Keywords: equations tight; oil gas; wave equations; tight oil ... See more keywords
Dispersive estimates for 2D-wave equations with critical potentials
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DOI: 10.1016/j.aim.2022.108333
Abstract: We study the 2D-wave equation with a scaling-critical electromagnetic potential. This problem is doubly critical, because of the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In… read more here.
Keywords: estimates wave; critical potentials; equations critical; wave equations ... See more keywords
Unified compact ADI methods for solving nonlinear viscous and nonviscous wave equations
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DOI: 10.1016/j.cjph.2018.09.025
Abstract: Abstract In this paper, two unified alternating direction implicit (ADI) methods, based on the combination of fourth-order compact difference for the approximations of the second spatial derivatives with approximation factorization of difference operators, are presented… read more here.
Keywords: viscous nonviscous; nonviscous wave; nonlinear viscous; adi methods ... See more keywords
Linearization of wave equations
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DOI: 10.1016/j.ijleo.2016.11.073
Abstract: Abstract We explore the ways to linearize the wave equations. Special emphasis is paid to the Klein–Gordon equation for a spin-0 relativistic particle and the Helmholtz equation governing scalar optics. Owing to the mathematical similarity,… read more here.
Keywords: optics; linearization wave; beam optics; wave equations ... See more keywords
Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions
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DOI: 10.1016/j.jde.2018.01.015
Abstract: Abstract The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of… read more here.
Keywords: smooth solutions; solutions null; boundary conditions; neumann boundary ... See more keywords