scholarly journals An abstract doubly nonlinear equation with a measure as initial value

2007 ◽  
Vol 331 (1) ◽  
pp. 308-328 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Veli-Matti Hokkanen
Keyword(s):  
Nonlinear Equation ◽  
Initial Value ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Equation

scholarly journals Long-Term Damped Dynamics of the Extensible Suspension Bridge

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Ivana Bochicchio ◽  
Claudio Giorgi ◽  
Elena Vuk
Keyword(s):  
Nonlinear Equation ◽  
Global Attractor ◽  
Axial Load ◽  
Suspension Bridge ◽  
External Source ◽  
Optimal Regularity ◽  
Absorbing Sets ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Equation

This work is focused on the doubly nonlinear equation , whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness . When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load and stiffness . For a general external source , we prove the existence of bounded absorbing sets. When is time-independent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.

Intrinsic scaling method for doubly nonlinear parabolic equations and its application

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Masashi Misawa ◽  
Kenta Nakamura
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Large Data ◽  
Nonlinear Parabolic Equations ◽  
Sobolev Type ◽  
Scaling Method ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Equation ◽  
Doubly Nonlinear Parabolic Equation

Abstract In this article, we consider a fast diffusive type doubly nonlinear parabolic equation, called 𝑝-Sobolev type flows, and devise a new intrinsic scaling method to transform the prototype doubly nonlinear equation to the 𝑝-Sobolev type flows. As an application, we show the global existence and regularity for the 𝑝-Sobolev type flows with large data.

scholarly journals The Local Stability of Solutions for a Nonlinear Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Haibo Yan ◽  
Ls Yong
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlinear Equation ◽  
Local Stability ◽  
Nonlinear Partial Differential Equation ◽  
Strong Solutions ◽  
Stability Of Solutions ◽  
Initial Value ◽  
Partial Differential

The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the spaceL1(R)by assuming that the initial value only lies in the spaceL1(R)∩L∞(R).

scholarly journals Conditions for the Existence of Global Solutions to Doubly Nonlinear Advection-diffusion Equations

2020 ◽  
Vol 21 (1) ◽  
pp. 83
Author(s):  
Jocemar Q. Chagas ◽  
Patrícia L. Guidolin ◽  
Paulo R. Zingano
Keyword(s):  
Initial Data ◽  
Initial Value Problem ◽  
Global Solutions ◽  
Critical Value ◽  
Initial Value ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Advection Term ◽  
Nonlinear Advection ◽  
Doubly Nonlinear

 In this work, we consider a initial-value problem for an doubly non linear advection-diffusion equation, and we present a critical value of κ up to wich the initial-value problem has global solution independent of the initial data u0, and from which global solutions may still exists, but from initial data u0 satisfying certain conditions. For this, we suppose that the function f(x,t,u) in the advection term, writted in the divergent form, satisfies certain conditions about your variation in Rn, and we also use the decrease of the norm L1(Rn) and an control for the norm L∞(Rn) of solution u(·,t). 

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