Wave equations with time-dependent dissipation II. Effective dissipation

By Jens Wirth. 2006

248 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc8b0286088a151a5c5df73f4af1af5424b5895c

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Citations in the corpus

The threshold of effective damping for semilinear wave equations (2015, background): “t/ut satisfying suitable assumptions [8, 9], in particular, if b.”
Diffusion phenomenon in Hilbert spaces and applications (2011, background): “Interpretation of the diffusion phenomenon and prior results The diffusion phenomenon encompasses a wide class of estimates that compare the long time behavior of solutions of the damped wave equation with the corresponding solutions of the heat equation.”
On the global solution problem for semilinear generalized Tricomi equations, I (2015, methodology): “icitly a critical value pc(µ,n) for µ≈ 1 so that problem (1.8) has a global small data solution ufor p>pc(µ,n), while solution uof (1.8) generally blows up in ﬁnite time when 1 <p≤ pc(µ,n) (see [2, 3, 12, 18, 26, 27]). Motivated by the techniques in [9] and this paper, we shall systematically ”
The Threshold between Effective and Noneffective Damping for Semilinear Waves (2012, background): “On the other hand, if b(t) is a sufficiently smooth function satisfying lim supt→∞ tb(t) < 1 then the dissipation is non effective [27].”
On the global existence and blowup of smooth solutions of 3-D compressible Euler equations with time-depending damping (2015, background): “6), it is shown in [23, 24] that the large-term behavior of solutions φ of L0(φ̇) = 0 depends on the value of λ.”
Weighted L2-estimates for dissipative wave equations with variable coefficients (2009, methodology): “Using Fourier analysis, Wirth [ W2 ], [W3], Reissig [MR], and Reissig and Wirth [RW] have obtained a series of sharp Lp Lq estimates including Z”
A classification of structural dissipations for evolution operators (2016, methodology): “When (12) holds, it is possible to investigate the chance to prove some modified scattering as done for (6) in [4], replacing the action of the multiplicative operator (7) with the action of the pseudo-differential operator (9).”