scholarly journals Strong solutions to a fourth order exponential PDE describing epitaxial growth

2022 ◽  
Vol 306 ◽  
pp. 220-250
Author(s):  
Brock C. Price ◽  
Xiangsheng Xu
Keyword(s):  
Epitaxial Growth ◽  
Fourth Order ◽  
Strong Solutions

scholarly journals Some fourth order nonlinear elliptic problems related to epitaxial growth

2013 ◽  
Vol 254 (6) ◽  
pp. 2515-2531 ◽  
Author(s):  
Carlos Escudero ◽  
Ireneo Peral
Keyword(s):  
Epitaxial Growth ◽  
Fourth Order ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

scholarly journals Local strong solutions to a quasilinear degenerate fourth-order thin-film equation

2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Christina Lienstromberg ◽  
Stefan Müller
Keyword(s):  
Thin Film ◽  
Fourth Order ◽  
Strong Solutions ◽  
Thin Film Equation ◽  
Local Strong Solutions

scholarly journals Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth

2020 ◽  
Vol 19 (12) ◽  
pp. 5581-5590
Author(s):  
Jun Zhou ◽  
Keyword(s):  
Epitaxial Growth ◽  
Fourth Order ◽  
Parabolic Pde

scholarly journals A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yang Liu ◽  
Wenke Li
Keyword(s):  
Thin Films ◽  
Epitaxial Growth ◽  
Fourth Order ◽  
Parabolic Equations ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Parabolic Equations ◽  
Potential Wells ◽  
Nonlinear Parabolic

<p style='text-indent:20px;'>In this paper, the initial-boundary value problem for a class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films is studied. By means of the theory of potential wells, the global existence, asymptotic behavior and finite time blow-up of weak solutions are obtained.</p>

Beyond the Mountain Pass: Some Applications

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Ireneo Peral
Keyword(s):  
Epitaxial Growth ◽  
Nonlinear Problem ◽  
Fourth Order ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
The Common ◽  
Zhang Model ◽  
Supercritical Problem

AbstractWe will survey three applications of the famous Mountain Pass Lemma by Antonio Ambrosetti and Paul H. Rabinowitz, [6]. Precisely, we will present some results on the following problems:A model of growth and roughening of surfaces, usually called Kardar-Parisi-Zhang model.A supercritical problem involving Hardy-Leray potential with the pole at the boundary.A fourth order nonlinear problem related to epitaxial growth.The common characteristic of all these problems is that we have some extra difficulties in order to apply the Mountain Pass Lemma.

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