scholarly journals Low Mach number limit of strong solutions for 3-D full compressible MHD equations with Dirichlet boundary condition

2017 ◽  
Vol 22 (11) ◽  
pp. 1-20
Author(s):  
Lan Zeng ◽  
◽  
Guoxi Ni ◽  
Yingying Li ◽  
Keyword(s):  
Boundary Condition ◽  
Mach Number ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Strong Solutions ◽  
Mhd Equations ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Compressible Mhd Equations

scholarly journals Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Jin-soo Hwang
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Continuous Dependence ◽  
Dirichlet Boundary ◽  
Strong Solutions ◽  
Function Spaces ◽  
Well Posedness ◽  
Continuous Dependence On Data ◽  
Strongly Damped ◽  
Weak And Strong Solutions

We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

On the Dispersive Estimate for the Dirichlet Schrödinger Propagator and Applications to Energy Critical NLS

2014 ◽  
Vol 66 (5) ◽  
pp. 1110-1142
Author(s):  
Dong Li ◽  
Guixiang Xu ◽  
Xiaoyi Zhang
Keyword(s):  
Boundary Condition ◽  
Fundamental Solution ◽  
Unit Ball ◽  
Dirichlet Boundary Condition ◽  
Obstacle Problem ◽  
Dirichlet Boundary ◽  
Radial Symmetry ◽  
Well Posedness ◽  
Robust Algorithm ◽  
Dispersive Estimate

AbstractWe consider the obstacle problem for the Schrödinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schrödinger propagator and give a robust algorithm to prove sharp L1 → L∞ dispersive estimates. We showcase the analysis in dimensions n = 5, 7. As an application, we obtain global well–posedness and scattering for defocusing energy-critical NLS on with Dirichlet boundary condition and radial data in these dimensions.

Sign in / Sign up

Export Citation Format

Share Document