Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric.
Blow up of solutions to semilinear wave equations.
Blow up of the solutions of nonlinear wave equation.
Blow-up of solutions to a nonlinear wave equation.
Blow-up of the solution to the initial-value problem in nonlinear three-dimensional hyperelasticity
We consider the initial value problem for the nonlinear partial differential equations describing the motion of an inhomogeneous and anisotropic hyperelastic medium. We assume that the stored energy function of the hyperelastic material is a function of the point x and the nonlinear Green-St. Venant strain tensor . Moreover, we assume that the stored energy function is with respect to x and . In our description we assume that Piola-Kirchhoff’s stress tensor depends on the tensor . This means...
Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent
In this paper, we show finite time blow-up of solutions of the p−wave equation in ℝN, with critical Sobolev exponent. Our work extends a result by Galaktionov and Pohozaev [4]
-well posedness of the Cauchy problem for quasi-linear hyperbolic equations with coefficients non-Lipschitz in time and smooth in space
In this paper we prove the -well posedness of the Cauchy problem for quasi-linear hyperbolic equations of second order with coefficients non-Lipschitz in t ∈ [0,T] and smooth in x ∈ ℝⁿ.
Carleman estimates for second-order hyperbolic equations.
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over , where is a sufficiently large time interval and a subdomain satisfies a non-trapping condition.
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over (0,T) x ω, where T > 0 is a sufficiently large time interval and a subdomain ω satisfies a non-trapping condition.
Cauchy data on a manifold
Characteristic initial value problem for hyperbolic systems of second order differential equations
Classical solutions of hyperbolic partial differential equations with implicit mixed derivative
Classical solutions of the perturbed wave equation with singular potential.
Comparison of solutions and successive approximations in the theory of the equation [Book]
Computation of the fundamental solution of electrodynamics for anisotropic materials
A new method for computation of the fundamental solution of electrodynamics for general anisotropic nondispersive materials is suggested. It consists of several steps: equations for each column of the fundamental matrix are reduced to a symmetric hyperbolic system; using the Fourier transform with respect to space variables and matrix transformations, formulae for Fourier images of the fundamental matrix columns are obtained; finally, the fundamental solution is computed by the inverse Fourier transform....
Constructing Orthogonal Curvilinear Meshes by Solving Initial Value Problems.
Continuous solutions of the problem of a string vibrating against an obstacle
Convolution Semigroups and Generalized Telegraph Equations.
Cubic Quasilinear wave equation and bilinear estimates