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In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L. T. P. Ngoc, N. T. Long (2011); L. X. Truong, L. T. P. Ngoc, N. T. Long (2009)) to get a convergent sequence at a rate of order $N \geq 2$ to a local unique weak solution of the above mentioned equation.

On a mixed nonlocal problem for a wave equation.

Beilin, Sergei A. (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On a nonlinear wave equation in unbounded domains.

Vasconcellos, Carlos Frederico (1988)

International Journal of Mathematics and Mathematical Sciences

On a parabolic strongly nonlinear problem on manifolds.

Marinho, A.O., Louredo, A.T., Lima, O.A. (2008)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

On a spatial problem of Darboux type for a second-order hyperbolic equation.

Kharibegashvili, S. (1995)

Georgian Mathematical Journal

On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms

Bui Duc Nam, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long (2022)

Mathematica Bohemica

We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.

On a weakly hyperbolic quasilinear mixed problem of second order

Piero d'Ancona, Mariagrazia Di Flaviano (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On an inverse problem for a linear hyperbolic integrodifferential equation.

Maurizio Grasselli (1994)

Forum mathematicum

On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables

Tomasz Człapiński (1997)

Annales Polonici Mathematici

We seek for classical solutions to hyperbolic nonlinear partial differential-functional equations of the second order. We give two theorems on existence and uniqueness for problems with nonlocal conditions in bounded and unbounded domains.

On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator.

Bouziani, Abdelfatah (2003)

Journal of Applied Mathematics

On periodic in the plane solutions of second order linear hyperbolic systems

Tariel Kiguradze (1997)

Archivum Mathematicum

Sufficient conditions for the problem $\frac{\partial^{2} u}{\partial x \partial y} = P_{0} (x, y) u + P_{1} (x, y) \frac{\partial u}{\partial x} + P_{2} (x, y) \frac{\partial u}{\partial y} + q (x, y), u (x + ω_{1}, y) = u (x, y), u (x, y + ω_{2}) = u (x, y)$ to have the Fredholm property and to be uniquely solvable are established, where $ω_{1}$ and $ω_{2}$ are positive constants and $P_{j} : R^{2} \to R^{n \times n}$ $(j = 0, 1 ...$

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Oblique derivative problems for second-order hyperbolic equations with degenerate curve.

Observability and controllability for a vibrating string with dynamical boundary control.

Observability and uniqueness theorem for a coupled hyperbolic system.

On a class of singular hyperbolic equation with a weighted integral condition.

On a Darboux type multidimensional problem for second-order hyperbolic systems.

On a global in time existence theorem of smooth solutions to an nonlinear wave equation with viscosity.

On a high-order iterative scheme for a nonlinear Love equation