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A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse

Gaetano Fichera (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective...

A classical solution weakened on the axis for a mixed problem of inhomogeneous hyperbolic equations.

Al-Momani, Raid (2003)

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

A nonlocal problem for fourth order hyperbolic equations with multiple characteristics.

Midodashvili, Bidzina (2002)

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

Addition to the Fichera paper

OLGA A. OLEINIK (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Asymptotic stability for a nonlinear evolution equation

Zhang Hongwei, Chen Guowang (2004)

Commentationes Mathematicae Universitatis Carolinae

We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation $(| u_{t} {|^{r - 2} u_{t})}_{t} - Δ u_{t t} - Δ u - δ Δ u_{t} = f (u)$ .

Blowup of solutions for evolution equations with nonlinear damping.

Wu, Shun-Tang, Tsai, Long-Yi (2006)

Applied Mathematics E-Notes [electronic only]

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 results for a nonlinear hyperbolic equation with Lewis function.

Tahamtani, Faramarz (2009)

Boundary Value Problems [electronic only]

Boundary stabilization of a hyperbolic equation with viscosity.

Cavalcanti, M.M. (1998)

The New York Journal of Mathematics [electronic only]

Caractérisation des problèmes mixtes hyperboliques bien posés

Jacques Chazarain (1972)

Mémoires de la Société Mathématique de France

Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation

Chen Guowang (1998)

Commentationes Mathematicae Universitatis Carolinae

The existence, uniqueness and regularity of the generalized local solution and the classical local solution to the periodic boundary value problem and Cauchy problem for the multidimensional coupled system of a nonlinear complex Schrödinger equation and a generalized IMBq equation $i ε_{t} + \nabla^{2} ε - u ε = 0,$ $u_{...}$

Darboux and Goursat type problems in the trihedral angle for hyperbolic type equations of third order

Otari Jokhadze (1997) Rendiconti del Seminario Matematico della Università di Padova

Determination of point sources in vibrating beams by boundary measurements: Identifiability, stability, and reconstruction results.

Nicaise, Serge, Zair, Ouahiba (2004) Electronic Journal of Differential Equations (EJDE) [electronic only]

Die Lösung der partiellen Differentialgleichung $u_{x x t t} = A (t, x) u_{x x} + B (t, x) u_{t t}$ mit gewissen Nebenbedingungen

Věra Radochová (1973)

Časopis pro pěstování matematiky

Existence and asymptotic behaviour for a degenerate Kirchhoff -Carrier model with viscosity and nonlinear boundary conditions.

M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. A. Soriano, J. S. Prates Filho (2001)

Revista Matemática Complutense

The present paper studies the existence and uniqueness of global solutions and decay rates to a given nonlinear hyperbolic problem.

Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary.

Santos, M.L., Ferreira, J., Raposo, C.A. (2005)

Abstract and Applied Analysis

Currently displaying 1 – 20 of 61