Local Existence of Solutions of the Dirichlet Initial-Boundary Value Problem for Incompressible Hypoelastic Materials

1990 ◽  
Vol 21 (6) ◽  
pp. 1369-1385 ◽  
Author(s):  
Michael Renardy
Keyword(s):  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Local Existence Of Solutions

FRACTIONAL LANDAU–GINZBURG EQUATIONS ON A SEGMENT

2008 ◽  
Vol 10 (06) ◽  
pp. 1151-1181
Author(s):  
ELENA I. KAIKINA
Keyword(s):  
Global Existence ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Existence Of Solutions ◽  
Asymptotic Representation Of Solutions ◽  
Representation Of Solutions ◽  
Initial Boundary Value

We study the initial-boundary value problem for the fractional Landau–Ginzburg equations on a segment. The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem and to find the main term of the asymptotic representation of solutions.

GLOBAL WEAKLY DISCONTINUOUS SOLUTIONS TO THE MIXED INITIAL–BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

2009 ◽  
Vol 19 (07) ◽  
pp. 1099-1138 ◽  
Author(s):  
ZHI-QIANG SHAO
Keyword(s):  
Boundary Value Problem ◽  
A Priori Estimates ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Local Existence ◽  
Discontinuous Solution ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Quasilinear Hyperbolic Systems ◽  
Initial Boundary Value

In this paper, we consider the mixed initial–boundary value problem for first-order quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space {(t, x) | t ≥ 0, x ≥ 0}. Based on the fundamental local existence results and global-in-time a priori estimates, we prove the global existence of a unique weakly discontinuous solution u = u(t, x) with small and decaying initial data, provided that each characteristic with positive velocity is weakly linearly degenerate. Some applications to quasilinear hyperbolic systems arising in physics and other disciplines, particularly to the system describing the motion of the relativistic closed string in the Minkowski space R1+n, are also given.

Upper Estimate of the Interval of Existence of Solutions of a Nonlinear Timoshenko Equation

1997 ◽  
Vol 4 (3) ◽  
pp. 219-222
Author(s):  
Drumi Bainov ◽  
Emil Minchev
Keyword(s):  
Growth Rate ◽  
Initial Data ◽  
Boundary Value Problem ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Upper Estimate

Abstract Solutions to the initial-boundary value problem for a nonlinear Timoshenko equation are considered. Conditions on the initial data and nonlinear term are given so that solutions to the problem under consideration do not exist for all t > 0. An upper estimate of the t-interval of the existence of solutions is obtained. An estimate of the growth rate of the solutions is given.

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