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
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