An analytical study of Kuznetsov's equation: diffusive solitons, shock formation, and solution bifurcation

An abstract semigroup approach to the third‐order Moore–Gibson–Thompson partial differential equation arising in high‐intensity ultrasound: structural decomposition, spectral analysis, exponential stability

“…This, notoriously, leads to the paradox of infinite speed of propagation. To avoid this pathology within nonlinear acoustics, [2,3] has then introduced alternative constitutive relations, such as the Maxwell-Cattaneo's Law to replace the Fourier Law. This latter effort then leads to a nonlinear third-order Jordan-Moore-Gibson-Thompson equation [2,3]:for suitable constants, where is the velocity potential of the acoustic phenomenon described on some bounded R 3 -domain.…”

“…To avoid this pathology within nonlinear acoustics, [2,3] has then introduced alternative constitutive relations, such as the Maxwell-Cattaneo's Law to replace the Fourier Law. This latter effort then leads to a nonlinear third-order Jordan-Moore-Gibson-Thompson equation [2,3]:for suitable constants, where is the velocity potential of the acoustic phenomenon described on some bounded R 3 -domain. The left hand side (LHS) of Equation (1.1) is the linearized component, yielding the linearized equationsupplemented by boundary conditions and initial conditions, which in [1] is referred to as the Moore-Gibson-Thompson (M-G-T) Equation.The physical meaning of the constants in Equation (1.2) is the following: is a positive constant accounting for relaxation; c is the speed of sound; b D ı C c 2 , where ı is the diffusivity of the sound.…”

Thermal effects on nonlinear acceleration waves in the Biot theory of porous media

“…Chen [29], and so we give minimal details of the calculations. One employs the constitutive theory (8) and (9) in equations (4), (5) and (7) and then we take the jumps of the resulting equations. We find that…”

“…The topic of wave propagation in porous and acoustic media is one of great interest in the current research literature, see e.g. Biot [1], Brunnhuber and Jordan [2], Christov [3], Christov and Jordan [4], Christov et al [5], Ciarletta and Straughan [6][7][8], Jordan [9][10][11][12][13][14], Jordan and Puri [15], Jordan and Saccomandi [16], Jordan et al [17,18], Paoletti [19], Rossmanith and Puri [20,21], Wei and Jordan [22].…”

Feedback control of the acoustic pressure in ultrasonic wave propagation

“…To name but a few, lithotripsy, thermoterapy, (ultrasound) welding, sonochemistry; cf., e.g., [15]. The excitation of induced acoustic fields in order to attain a given task, such as destroying certain 'obstacles' (stones in kidneys or deposits resulting from chemical reactions), renders the presence of control functions within the model well-founded.The subject of the present investigation is an optimal control problem for a third order in time PDE, referred to in the literature as the Moore-Gibson-Thompson equation, which is the linearization of the Jordan-Moore-Gibson-Thompson (JMGT) equation, arising in the modeling of ultrasound waves; see [16,17], [19], [34]. In contrast with the renowned Westervelt ([36]) and Kuznetsov equations, the JMGT equation displays a finite speed of propagation of acoustic waves, thereby providing a solution to the infinite speed of propagation paradox.…”