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
Pullback Attractors for a Damped Semilinear Wave Equation with Delays
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DOI: 10.1007/s10114-018-7420-3
Abstract: In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g(t, ut) may be driven by a function with very weak assumptions,… read more here.
Keywords: semilinear wave; pullback attractors; attractors damped; damped semilinear ... 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
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
Almost global existence for semilinear wave equations with mixed nonlinearities in four space dimensions
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.10.058
Abstract: Abstract We study the long time existence for the small-amplitude semilinear wave equations with mixed nonlinearities of the form c 1 | u t | p + c 2 u 2 with p ≥ 2… read more here.
Keywords: existence; semilinear wave; mixed nonlinearities; equations mixed ... See more keywords
A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2022.126266
Abstract: 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… read more here.
Keywords: blow results; equations sitter; sitter anti; results semilinear ... See more keywords
Global existence and blowup of smooth solutions to the semilinear wave equations in FLRW spacetime
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DOI: 10.1063/5.0181173
Abstract: We are interested in the semilinear wave equations evolving in the expanding spacetimes with Friedmann–Lemaître–Robertson–Walker (FLRW) metric. By the weighted energy estimate, we show that when the nonlinearity depends on the time derivative of the… read more here.
Keywords: equations flrw; semilinear wave; global existence; wave equations ... See more keywords
On the Defocusing Semilinear Wave Equations in Three Space Dimension with Small Power
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DOI: 10.1093/imrn/rnab260
Abstract: By introducing new weighted vector fields as multipliers, we derive quantitative pointwise estimates for solutions of defocusing semilinear wave equation in $\mathbb {R}^{1+3}$ with pure power nonlinearity for all $1 read more here.
Keywords: three space; semilinear wave; equations three; power ... See more keywords