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Special Session 120

Linear and Nonlinear fourth order PDE's

Organizer(s):

Jan Cholewa

Filippo Gazzola

arober@mat.ucm.es

Introduction:

Fourth order PDEs problems have a wide range of applications, from elasticity to phase transitions, to mention just a few. However compared with similar second order problems, they usually do not have maximum principles, a crucial tool that pushed forward the theory of such problems. Therefore, the mathematical theory for fourth order problems has not reached the same degree of development although it has witnessed a growing interest in recent times. This session is devoted to present some recent advances on higher order partial differential equations and is focused on various aspects of both elliptic and evolutionary models.

List of abstracts Go Back
Name	Country	Title
Tomasz W Dlotko	Poland	Korteweg-de Vries-Burgers system in R^N
Jan Cholewa	Poland	On the Cahn-Hilliard equation in $H^1({\mathbb R}^N)$
Carlos Escudero	Spain	Existence and non-existence of solutions for a biharmonic partial differential equation with a Hessian nonlinearity
Filippo Gazzola	Italy	Quasilinear fourth order elliptic equations modeling suspension bridges
Yongda Wang	Italy	Remarks on a class of fourth order hyperbolic partial differential equations
Futoshi Takahashi	Japan	Local asymptotic nondegeneracy for multi-bubble solutions to the biharmonic Liouville-Gel'fand problem in dimension four
Pier Domenico Lamberti	Italy	Reissner Mindlin system and Biharmonic equation: a spectral shape sensitivity analysis
Alberto A Ferrero	Italy	Existence and stability properties of entire solutions to a polyharmonic equation with exponential nonlinearity
Jose M Arrieta	Spain	Spectral stability results for higher-order operators under perturbations of the domain
Michele M Bartuccelli	England	Explicit estimates on the torus for the supnorm of solutions of the Swift and Hohenberg Equation in one and two space dimensions
Anibal Rodriguez-Bernal	Spain	On the dissipativity of some fourth order problems in $\R^N$
Mario Bukal	Croatia	Quantum diffusion equations
Paolo Caldiroli	Italy	Entire solutions for a class of fourth order semilinear elliptic equations with weights
Alexander A Kovalevsky	Ukraine	Proper entropy solutions for nonlinear elliptic fourth-order equations with a strengthened coercivity and $L^1$-data
Carlos Quesada	Spain	Fourth order linear and nonlinear parabolic equations in Banach spaces in $\mathbb{R}^N$ with low regularity initial data
Salomon Alarcon	Chile	A Paneitz-type problem in pierced domain
Michael Winkler	Germany	A fourth order parabolic equation modeling epitaxial thin film growth