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Displaying 21 – 40 of 58

Blow-Up of Solutions of Nonlinear Wave Equations in Three Space Dimensions.

Fritz John (1979)

Manuscripta mathematica

Blow-up of solutions to a nonlinear wave equation.

Georgiev, Svetlin Georgiev (2004)

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

Blow-Up of solutions to nonlinear wave equations in two space dimensions.

Rentaro Agemi (1991)

Manuscripta mathematica

Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation

Qingyong Gao, Fushan Li, Yanguo Wang (2011)

Open Mathematics

In this paper, we consider the nonlinear Kirchhoff-type equation $u_{t t} + M ({∥D^{m} u (t)∥}_{2}^{2}) {(- Δ)}^{m} u + {|u_{t}|}^{q - 2} u_{t} = {|u_{t}|}^{p - 2} u$ with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.

Blow-up of the solution to the initial-value problem in nonlinear three-dimensional hyperelasticity

J. A. Gawinecki, P. Kacprzyk (2008)

Applicationes Mathematicae

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 $e_{j k}$ . Moreover, we assume that the stored energy function is $C^{\infty}$ with respect to x and $e_{j k}$ . In our description we assume that Piola-Kirchhoff’s stress tensor $p_{j k}$ depends on the tensor $e_{j k}$ . This means...

Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping

Lorena Bociu, Irena Lasiecka (2008)

Applicationes Mathematicae

We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.

Blow-up results for a nonlinear hyperbolic equation with Lewis function.

Tahamtani, Faramarz (2009)

Boundary Value Problems [electronic only]

Blow-up results for nonlinear hyperbolic inequalities

Stanislav Pohozaev, Laurent Véron (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

S. Ibrahim, A. Lyaghfouri (2012)

Mathematical Modelling of Natural Phenomena

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]