scholarly journals Almost global existence for the initial value problem of nonlinear elastodynamic system

2008 ◽  
Vol 339 (1) ◽  
pp. 517-529 ◽  
Author(s):  
Xin Jie ◽  
Qin Tiehu
Keyword(s):  
Global Existence ◽  
Initial Value Problem ◽  
Initial Value

scholarly journals Remarks on the critical nonlinear high-order heat equation

2019 ◽  
Vol 26 (1/2) ◽  
pp. 127-152
Author(s):  
Tarek Saanouni
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
High Order ◽  
Well Posedness ◽  
Potential Well ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Nonlinear High Order

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

scholarly journals Global existence for abstract nonlinear Volterra–Fredholm functional integrodifferential equation

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
M. B. Dhakne ◽  
Kishor D. Kucche
Keyword(s):  
Global Existence ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
A Priori ◽  
A Priori Bounds ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Fredholm Functional

AbstractIn the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.

HOPF SOLUTIONS TO A FLUID-ELASTIC INTERACTION MODEL

2008 ◽  
Vol 18 (02) ◽  
pp. 215-269 ◽  
Author(s):  
M. GUIDORZI ◽  
M. PADULA ◽  
P. I. PLOTNIKOV
Keyword(s):  
Global Existence ◽  
Existence Theorem ◽  
Initial Value Problem ◽  
Interaction Model ◽  
Elastic Interaction ◽  
Initial Condition ◽  
Two Dimensional ◽  
Initial Value ◽  
Global Existence Theorem ◽  
Model Equations

In this paper, we give a global existence theorem of weak solutions to model equations governing interaction fluid structure in a two-dimensional layer, cf. Refs. 8 and 14. To our knowledge this is the first existence theorem of global in time solutions for such model. The interest of our result is double because, first, we change the original initial value problem by deleting one initial condition, second, we construct a solution through the classical Galerkin method for which several computing codes have been constructed.

scholarly journals Global existence of small displacement solutions for Hookean incompressible viscoelasticity in 3D

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Boyan Jonov ◽  
Paul Kessenich ◽  
Thomas C. Sideris
Keyword(s):  
Global Existence ◽  
Initial Value Problem ◽  
Strong Solutions ◽  
Small Displacement ◽  
Initial Value ◽  
Global Strong Solutions ◽  
Three Space

<p style='text-indent:20px;'>The initial value problem for incompressible Hookean viscoelastic motion in three space dimensions has global strong solutions with small displacements.</p>

Global spatially periodic solutions to the Ginzburg–Landau equation

1988 ◽  
Vol 110 (3-4) ◽  
pp. 263-273 ◽  
Author(s):  
Yisong Yang
Keyword(s):  
Global Existence ◽  
Periodic Solutions ◽  
Initial Value Problem ◽  
Landau Equation ◽  
Initial Value ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Existence And Nonexistence ◽  
Spatially Periodic

SynopsisIn this paper we study the global existence and nonexistence of spatially periodic solutions to the initial value problem of the Ginzburg–Landau equation.

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