Global Existence of Solutions of Noncharacteristic Mixed Problems to Nonlinear Symmetric Dissipative Systems of the First Order

1989 ◽  
pp. 688-697
Author(s):  
W. M. Zajaczkowski
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Dissipative Systems ◽  
First Order ◽  
Mixed Problems ◽  
Global Existence Of Solutions

scholarly journals The Muskat problem with surface tension and equal viscosities in subcritical $$L_p$$-Sobolev spaces

2021 ◽  
Author(s):  
Anca-Voichita Matioc ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Well Posedness ◽  
Global Existence Of Solutions ◽  
Muskat Problem ◽  
The Mathematical Model ◽  
Quasilinear Parabolic

AbstractIn this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $$W^s_p(\mathbb {R})$$ W p s ( R ) , where $${p\in (1,2]}$$ p ∈ ( 1 , 2 ] and $${s\in (1+1/p,2)}$$ s ∈ ( 1 + 1 / p , 2 ) . This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $$W^{\overline{s}-2}_p(\mathbb {R})$$ W p s ¯ - 2 ( R ) , where $${\overline{s}\in (1+1/p,s)}$$ s ¯ ∈ ( 1 + 1 / p , s ) . Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.

scholarly journals Global existence of solutions for a multi-phase flow: A drop in a gas-tube

2016 ◽  
Vol 13 (02) ◽  
pp. 381-415
Author(s):  
Debora Amadori ◽  
Paolo Baiti ◽  
Andrea Corli ◽  
Edda Dal Santo
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Inviscid Fluid ◽  
Phase Flow ◽  
Lagrangian Coordinates ◽  
Large Initial Data ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Multi Phase Flow ◽  
Multi Phase

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

scholarly journals Global existence of solution for multidimensional generalized double dispersion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaoqiang Dai
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Dispersion Equation ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
New Methods ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
Double Dispersion

Abstract In this paper, we study the Cauchy problem of multidimensional generalized double dispersion equation. To prove the global existence of solutions, we introduce some new methods and ideas, and fill some gaps in the established results.

scholarly journals On the System of Coupled Nondegenerate Kirchhoff Equations with Distributed Delay: Global Existence and Exponential Decay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Salem Alkhalaf ◽  
Ibrahim Mekawy ◽  
...  
Keyword(s):  
Global Existence ◽  
Exponential Stability ◽  
Galerkin Method ◽  
Exponential Decay ◽  
Energy Method ◽  
Existence Of Solutions ◽  
Distributed Delay ◽  
Stability Result ◽  
Kirchhoff Equations ◽  
Global Existence Of Solutions

This paper studies the system of coupled nondegenerate viscoelastic Kirchhoff equations with a distributed delay. By using the energy method and Faedo-Galerkin method, we prove the global existence of solutions. Furthermore, we prove the exponential stability result.

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