ON QUALITATIVE PROPERTIES OF SOLUTIONS OF QUASILINEAR MIXED PROBLEMS FOR EQUATIONS OF PARABOLIC TYPE

1977 ◽  
Vol 33 (3) ◽  
pp. 427-446 ◽  
Author(s):  
T I Zelenjak
Keyword(s):  
Parabolic Type ◽  
Qualitative Properties ◽  
Mixed Problems ◽  
Qualitative Properties Of Solutions

scholarly journals Well-Posedness and Stability Results for Some Periodic Muskat Problems

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Bogdan-Vasile Matioc
Keyword(s):  
Surface Tension ◽  
Blow Up ◽  
Parabolic Type ◽  
Well Posedness ◽  
Equilibrium Solutions ◽  
Qualitative Properties ◽  
Muskat Problem ◽  
Quasilinear Parabolic Problem ◽  
The Stability ◽  
Qualitative Properties Of Solutions

Abstract We study the two-dimensional Muskat problem in a horizontally periodic setting and for fluids with arbitrary densities and viscosities. We show that in the presence of surface tension effects the Muskat problem is a quasilinear parabolic problem which is well-posed in the Sobolev space $$H^r({\mathbb {S}})$$ H r ( S ) for each $$r\in (2,3)$$ r ∈ ( 2 , 3 ) . When neglecting surface tension effects, the Muskat problem is a fully nonlinear evolution equation and of parabolic type in the regime where the Rayleigh–Taylor condition is satisfied. We then establish the well-posedness of the Muskat problem in the open subset of $$H^2({\mathbb {S}})$$ H 2 ( S ) defined by the Rayleigh–Taylor condition. Besides, we identify all equilibrium solutions and study the stability properties of trivial and of small finger-shaped equilibria. Also other qualitative properties of solutions such as parabolic smoothing, blow-up behavior, and criteria for global existence are outlined.

Qualitative properties of solutions to set optimization problems

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Lam Quoc Anh ◽  
Nguyen Huu Danh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Qualitative Properties ◽  
Qualitative Properties Of Solutions

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Radially symmetric solutions to the Hénon–Lane–Emden system on the critical hyperbola

2014 ◽  
Vol 16 (03) ◽  
pp. 1350030 ◽  
Author(s):  
Roberta Musina ◽  
K. Sreenadh
Keyword(s):  
Variational Methods ◽  
Existence Results ◽  
Qualitative Properties ◽  
Radially Symmetric Solutions ◽  
Qualitative Properties Of Solutions

We use variational methods to study the existence of non-trivial and radially symmetric solutions to the Hénon–Lane–Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative properties of solutions and non-existence results.

Sign in / Sign up

Export Citation Format

Share Document