Nonstationary boundary value problems for wave equation and their generalized solutions
L. A. Alexeyeva
Abstract
The multivariate analogue of Dalamber's equation in the space of generalized functions is considered. The method of generalized functions for the building of solutions of nonstationary boundary value problems for wave equations in spaces of different dimensions is elaborated. Dynamic analogues of Green and Gauss formulas for solutions of wave equation in the space of generalized functions are built. Their regular integral representations and singular boundary integral equations for solving the nonstationary problems are constructed for the spaces of the dimensions 1,2,3. The method of obtaining of conditions on fronts of shock waves is stated.
Create a lesson
Related papers
Monotonicity of the propagation speed with respect to the diffusion in a Lotka-Volterra competition-diffusion system
Cyrille Kenne
Sign-preserving solutions to the Tzitzéica equation on lattice graphs
Pengxiu Yu, Yiping Zhang
Concavity and other properties of the entropy on manifolds
Xuenan Fu, Juanling Lu, Qi S. Zhang
The Higher-Dimensional Nitsche Conjecture: Sharp Bounds and Rigidity
Bin Deng, Jiahuan Li, Yilu Liu et al.
The complete spectrum of the linearized p-Laplacian at a Sobolev extremal
Yitian Zhang
Rigidity and existence of Busemann profiles for the Allen--Cahn equation on Cartan--Hadamard manifolds
Luis Eduardo Osorio-Acevedo, Álvaro Jaramillo