Critical Exponent for a Nonlinear Wave Equation with Damping

By Grozdena Todorova, Borislav Yordanov. 2000

457 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c7ed9491910f5c8c8b4c5a6e928916e700c0576d

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In Control and Systems Engineering

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation (2010, methodology): “Also, as for the study of decay properties for dissipative hyperbolic-type equations, we refer to [19, 23, 27, 33] for damped wave equations, [34] for wave equations with nonlinear dissipation and [12, 20, 26] for wave equations of memory-type dissipation.”
Damped wave equation with super critical nonlinearities (2004, background): “For higher space dimensions, in paper [11], it was proved the global existence and energy decay estimates of solutions to the Cauchy problem for the damped wave equation (2) with sufficiently small initial data having a compact support, in the case ρ > 1 + 2 n .”
Energy decay for the Cauchy problem of the linear wave equation of variable coefficients with dissipation (2009, background): “For the Cauchy problem, see [21, 28–30] and many other papers.”
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption (2006, methodology): “1 The weighted energy method developed in Todorova and Yordanov [33] is applied to the proof by combining the local existence theorem and the a priori estimates.”
Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption (2006, background): “The weight function is chosen as (later a is determined as 1 / 4), which is a modiﬁcation of the weight introduced in Todorova and Yordanov [32].”
L 1 Estimates for Oscillating Integrals Related to Structural Damped Wave Models (2013, background): “In both cases Lp−Lq estimates for the solutions are well understood; see [4–7, 10] and [11] for the case σ = 0 (linear or semi-linear models) and [8] for the case σ = 1.”