Small vertical vibrations of strings with moving ends.

On a nonlinear wave equation involving the term : Linear approximation and asymptotic expansion of solution in many small parameters

“…, p), is established in Section 4. This result is a relative generalization of [4][5][6][7]10,11,9,[24][25][26][27][28]20,21,29,22,12,23,30,2,[14][15][16][17].…”

“…(1.4) received much attention where an abstract framework to the problem was proposed. We refer the reader to, e.g., Cavalcanti et al [4][5][6], Ebihara, Medeiros and Miranda [7], Miranda et al [8], Lasiecka and Ong [9], Hosoya, Yamada [10], Larkin [11], Medeiros [12], Menzala [13], Park et al [14,15], Rabello et al [16], Santos et al [17], for many interesting results and further references. A survey of the results about the mathematical aspects of Kirchhoff model can be found in Medeiros, Limaco and Menezes [18,19].…”

Linear Approximation and Asymptotic Expansion of Solutions in Many Small Parameters for a Nonlinear Kirchhoff Wave Equation with Mixed Nonhomogeneous Conditions

“…4. This result is a relative generalization of [1,5,6,8,9,[12][13][14][15][16][17][18][23][24][25][26][27][28][29][30][31].…”

“…After the work of Lions, for example see [11], (1.5) received much attention where an abstract framework to the problem was proposed. We refer the reader to, e.g., J.J. Bae, M. Nakao [1], Cavalcanti et al [2,3], Ebihara, Medeiros and Miranda [5], Hosoya and Yamada [6], Lasiecka and Ong [9], Miranda et al [22], Menzala [21], Park et al [25,26], Rabello et al [28], Santos et al [29], Yamada [31] for many interesting results and further references.…”

Existence, blow-up and exponential decay estimates for the nonlinear Kirchhoff-Carrier wave equation in an annular with nonhomogeneous Dirichlet conditions

“…(1.1) received much attention. We refer the reader to, e.g., Cavalcanti et al [1], [2], Ebihara, Medeiros and Miranda [4], Miranda et al [15], Lasiecka and Ong [8], Hosoya, Yamada [5], Larkin [7], Long et al [10]- [12], Medeiros [14], Menzala [16], Messaoudi [17], Ngoc et al [18]- [22], Park et al [23], [24], Rabello et al [25], Santos et al [26], Truong et al [28], for many interesting results and further references. In these works, the results concerning local existence, global existence, asymptotic expansion, asymptotic behavior, decay and blow-up of solutions have been examined.…”