# UNIQUENESS OF GENERALIZED SOLUTIONS TO NONLINEAR WAVE EQUATIONS

## Related Articles

- Blow Up of Solutions to the Cauchy Problem for Nonlinear Wave Equations. Zhou, Yi // Chinese Annals of Mathematics;Jul2001, Vol. 22 Issue 3, p275
The author proves blow up of solutions to the Cauchy problems of certain nonlinear wave equations and, also, estimates the time when the blow up occurs.

- On the Classification of Initial Data for Nonlinear Wave Equations. Gu, Chaohao // Chinese Annals of Mathematics;Apr2002, Vol. 23 Issue 2, p205
The purpose of the present paper is to call for attention to the following question: Which of the initial data (nonsmall) admit global smooth solutions to the Cauchy problem for nonlinear wave equations. A few cases and examples are sketched, showing that the general answer of this question may...

- The One-Dimensional Inverse Problem in Photoacoustics. Numerical Testing. Langemann, D.; Mikhaylov, A. S.; Mikhaylov, V. S. // Journal of Mathematical Sciences;Dec2019, Vol. 243 Issue 5, p726
The problem of reconstruction of the Cauchy data for the wave equation in â„1 from the measurements of its solution on the boundary of a finite interval is considered. This is a one-dimensional model for the multidimensional problem of photoacoustics, which was studied previously. The...

- ON THE UNIFORMLY CONTINUITY OF THE SOLUTION MAP FOR TWO DIMENSIONAL WAVE MAPS. Georgiev, Svetlin Georgiev; Georgieva, Penka Vasileva // Electronic Journal of Qualitative Theory of Differential Equatio;Dec2003, p1
The aim of this paper is to analyze the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid HÂ² that is embedded in RÂ³. The initial data are in HÂ¹ x LÂ². We prove that the solution map is not uniformly...

- Simulation of unusual direction of tsunami waves in terms of elementary functions. Volkov, B.; Sekerzh-Zen’kovich, S. // Fluid Dynamics;Dec2009, Vol. 44 Issue 6, p896
The wave directivity is studied by analyzing asymptotic solutions of the nondispersive piston tsunami model used on the assumption that the process id linear. In the model initial perturbations of the power-function type are considered. Asymptotic formulas for the wave profiles are derived in...

- Energy decay for the Cauchy problem of the linear wave equation of variable coefficients with dissipation. Yao, Pengfei // Chinese Annals of Mathematics;Jan2010, Vol. 31 Issue 1, p59
Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In...

- A Stability Estimate for a Solution to the Wave Equation with the Cauchy Data on a Timelike Cylindrical Surface. Romanov, V. // Siberian Mathematical Journal;Sep2005, Vol. 46 Issue 5, p925
We consider the linear wave equation in a domain of the x, t-space bounded from above and below by some smooth surfaces and from the sides by a cylindrical surface with generator parallel to the t-axis. We study the Cauchy problem for this equation with data on a piece of the timelike...

- Global solutions and blow-up phenomena for the periodic b-equation. Zhang, S.; Yin, Z. // Journal of the London Mathematical Society;Oct2010, Vol. 82 Issue 2, p482
In the paper, we mainly study the Cauchy problem of a family of asymptotically equivalent shallow water wave equations, the so called periodic b-equation. We first establish the local well-posedness for the periodic b-equation. Then we derive the precise blow-up scenario and present two blow-up...

- The Cauchy problem for the diffusion-wave equation with the Caputo partial derivative. Voroshilov, A.; Kilbas, A. // Differential Equations;May2006, Vol. 42 Issue 5, p638
The article studies the cauchy problem for the diffusion-wave equation with the caputo partial derivative. Laplace and Fourier transforms of the function u(x,t) were used. Operators are mutually inverse on sufficiently smooth functions u(x,t). Proof of the solution of the problem in terms of the...