On a quasilinear wave equation with nonlinear damping

1988 ◽  
Vol 110 (3-4) ◽  
pp. 227-239 ◽  
Author(s):  
Dang Dinh Hai
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Nonlinear Damping ◽  
Quasilinear Wave Equation ◽  
Uniqueness Of The Solution ◽  
Global Existence And Uniqueness ◽  
Image Position

SynopsisWe prove the global existence and uniqueness of the solution of the initial and boundary value problem for the equationby using the classical Galerkin method when the forcing term and the initial data are in some sense small. The asymptotic behaviour of the solution as t → ∞ is also considered.

Boundary flow for the minimal surfaces in Rn with Plateau boundary condition

2005 ◽  
Vol 135 (3) ◽  
pp. 537-562
Author(s):  
Kung-Ching Chang ◽  
Jia-Quan Liu
Keyword(s):  
Boundary Condition ◽  
Initial Data ◽  
Global Existence ◽  
Minimal Surfaces ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Boundary Flow ◽  
Global Existence And Uniqueness

We introduce the notion of the boundary flow for minimal surfaces in Rn with Plateau boundary condition and establish the global existence and uniqueness of the flow as well as the continuous dependence on the initial data.

Boundary flow for the minimal surfaces in Rn with Plateau boundary condition

2005 ◽  
Vol 135 (3) ◽  
pp. 537-562 ◽  
Author(s):  
Kung-Ching Chang ◽  
Jia-Quan Liu
Keyword(s):  
Boundary Condition ◽  
Initial Data ◽  
Global Existence ◽  
Minimal Surfaces ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Boundary Flow ◽  
Global Existence And Uniqueness

We introduce the notion of the boundary flow for minimal surfaces in Rn with Plateau boundary condition and establish the global existence and uniqueness of the flow as well as the continuous dependence on the initial data.

scholarly journals On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
David Massatt
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Well Posedness ◽  
Two Dimensional ◽  
Periodic Domain ◽  
Uniqueness Of Solutions ◽  
Global Existence And Uniqueness ◽  
Sivashinsky Equation

<p style='text-indent:20px;'>We address the global existence and uniqueness of solutions for the anisotropically reduced 2D Kuramoto-Sivashinsky equations in a periodic domain with initial data <inline-formula><tex-math id="M1">\begin{document}$ u_{01} \in L^2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ u_{02} \in H^{-1 + \eta} $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M3">\begin{document}$ \eta &gt; 0 $\end{document}</tex-math></inline-formula>.</p>

scholarly journals Global existence and uniqueness of the solution to a nonlinear parabolic equation

2018 ◽  
Vol 14 (2) ◽  
pp. 7860-7863
Author(s):  
Alexander G. Ramm
Keyword(s):  
Parabolic Equation ◽  
Global Existence ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equation ◽  
Unique Global Solution ◽  
Nonlinear Parabolic ◽  
Uniqueness Of The Solution ◽  
Global Existence And Uniqueness

Consider the equation  u’ (t)  -  u + | u |p u = 0, u(0) = u0(x), (1), where u’ := du/dt , p = const > 0, x E R3, t > 0.  Assume that u0 is a smooth and decaying function,           ||u0|| =            sup             |u(x, t)|.                                         x E R3 ,t E R+      It is proved that problem (1) has a unique global solution and this solution satisfies the following estimate                              ||u(x, t)|| < c, where c > 0 does not depend on x, t.

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