References
- Beale JT, Rosencrans SI. Acoustic boundary conditions. Bull Amer Math Soc. 1974;80(6):1276–1278.
- Alcantara AA, Clark HR, Rincon MA. Theoretical analysis and numerical simulation for a hyperbolic equation with dirichlet and acoustic boundary conditions. Comput Appl Math. 2018;37:4772–4792.
- Abbas Z, Nicaise S. The multidimensional wave equation with generalized acoustic boundary conditions ii: polynomial stability. Siam J Control Optim. 2015;53:2582.2607
- Yamna B, Benyattou B. Existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions. Nonlinear Anal Theoret Methods Appl. 2014;97:191–209.
- Yamna B, Benyattou B. Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions. Acta Math Sinica Engl Ser. 2016;32(2):153–174.
- Cavalcanti MM, Cavalcanti V, Frota CL, et al. Stability for semilinear wave equation in an inhomogeneous medium with frictional localized damping and acoustic boundary conditions. SIAM J Control Optim. 2020;58(4):2411–2445.
- Graber PJ, Said-Houari B. On the wave equation with semilinear porous acoustic boundary conditions. J Differ Equ. 2012;252:4898–4941.
- Hao J, He WH. Energy decay of variable coefficient wave equation with nonlinear acoustic boundary conditions and source term. Math Methods Appl Sci. 2019;42:2109–2123.
- Li J, Chai S. Energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time-varying delay in the boundary feedback. Nonlinear Anal Theoret Methods Appl. 2015;112:105–117.
- Gao Y, Liang J, Xiao TJ. A new method to obtain uniform decay rates for multidimensional wave equations with nonlinear acoustic boundary conditions. SIAM J Control Optim. 2018;56(2):1303–1320.
- Ragusa MA, Razani A, Safari F. Existence of radial solutions for a p(x) -laplacian dirichlet problem. Adv Differ Equ. 2021;2021(215):1–14.
- Chaharlang MM, Ragusa MA, Razani A. Sequence of radially symmetric weak solutions for some nonlocal elliptic problem in Rn. Mediterranean J Math. 2020;17(2):1–12.
- Safari F, Razani A. Nonlinear nonhomogeneous neumann problem on the Heisenberg group. Appl Anal. 2020;14:1–4.
- Chaharlang MM, Razani A. Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition. Georgian Math J. 2020;28:429–438.
- Yao PF. Observability inequalities for wave equations with variable coefficients. Decision and Control, 1999. IEEE Conference on Proceedings of the 38th; 1999.
- Yao PF. Global smooth solutions for the quasilinear wave equation with boundary dissipation. J Differ Equ. 2007;241(1):62–93.
- Yao PF. Energy decay for the cauchy problem of the linear wave equation of variable coefficients with dissipation. Chinese Ann Math Ser B. 2010;0:0.
- Chai SG, Guo YH. Boundary stabilization of wave equations with variable coefficients and memory. Differ Integral Equ. 2004;17(5-6):669–680.
- Chen H, Luo P, Liu GW. Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity. J Math Anal Appl. 2015;422(1):84–98.
- Di HF, Shang YD, Song ZF. Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity. Nonlinear Anal Real World Appl. 2020;51:1–22.
- Chen H, Tian SY. Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity. J Differ Equ. 2015;258(12):4424–4442.
- Ding H, Zhou J. Global existence and blow-up for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. J Math Anal Appl. 2019;478(2):393–420.
- Liu HL, Liu ZS, Xiao QZ. Ground state solution for a fourth-order nonlinear elliptic problem with logarithmic nonlinearity. Appl Math Lett. 2018;79:176–181.
- Agarwal RP, Gala S, Ragusa MA. A regularity criterion in weak spaces to boussinesq equations. Math. 2020;8(6):920.
- Barros V, Nonato C, Raposo C. Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights. Electron Res Archive. 2020;28(1):205–220.
- Gala S, Galakhov E, Ragusa MA, et al. Beale-Kato-Majda regularity criterion of smooth solutions for the Hall-MHD equations with zero viscosity. Bulletin Brazilian Math Soc. 2021;1:1–13.
- Lasiecka I, Tataru D. Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differ Integral Equ. 1993;6(3):507–533.
- Graber PJ, Said-Houari B. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions. Appl Math Optim. 2012;66(1):81–122.
- Cavalcanti MM, Domingos C, Ryuichi F, et al. Uniform decay rate estimates for the semilinear wave equation in inhomogeneous medium with locally distributed nonlinear damping. Nonlinearity. 2018;31(9):4031–4064.
- Pazy A. Semigroups of linear operators and applications to partial differential equations. New York (NY): Springer-Verlag New York; 1983.
- Cavalcanti MM, Cavalcanti V, Martinez P. Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term. J Differ Equ. 2004;203(1):119–158.
- Lasiecka I, Triggiani R. Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions. Appl Math Optim. 1992;25(2):189–224.
- Simon J. Compact sets in the space Lp(0,T;B). Annalidi Matematica Pura Ed Applicata. 1986;146:65–96.