The Lp–Lq estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media

By Pierangelo Marcati, Kenji Nishihara. 2003

133 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ee51093eb831e6ee6ca1008222f5d38bce8dedac

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption (2006, methodology): “36) (see Matsumura [24] and [13,23,25,27]).”
$ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data (2017, background): “Based on the linear estimates (3), many mathematicians studied the global existence and the blow-up of solutions (see [9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23, 24, 27, 30, 34, 36, 37] and the references therein).”
New decay estimates for linear damped wave equations and its application to nonlinear problem (2004, unknown): “In a sense, we can say that the non-linear problem (6)–(8) also has a kind of di usion structure as in the linear case (for di usion phenomenon, see Ikehata [9], Ikehata– Nishihara [10], Karch [5], Marcati–Nishihara [20], Nishihara [4], and the references therein).”
Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (2007, background): “A huge amount of work has been done during many years around the special case of the dissipative (nonlinear) wave equation, see for instance [14, 24, 29] and references therein.”
A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations (2017, background): “This effect modifies the asymptotic profile of the solution to the corresponding linear problem so that it can be described by the solution to a heat equation with suitable initial data (see [23] and, later, [22, 30, 40]).”
Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption (2006, background): “See also Marcati and Nishihara [23] in 1-dimensional space, Hosono and Ogawa [15] in 2-dimensional space and Narazaki [25] in general space dimension and Ikehata [16], Ikehata and Nishihara [19], Chill and Haraux [3] in the abstract setting.”