Nonlinear Evolution Equations and Related Topics: Dedicated to Philippe Bénilan

ISBN-13: 9783764371074 / Angielski / Miękka / 2004 / 807 str.

Arendt, Wolfgang

Opis

Philippe Benilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. This present volume is dedicated to him and contains research papers written by highly distinguished mathematicians. They are all related to Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations. Special topics include: Hamilton-Jacobi equations, the porous medium equation, reaction diffusion systems, integro-differential equations and visco-elasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein Uhlenbeck operator. Also in this special volume, the legendary work of Benilan-Brezis on Thomas-Fermi Theory is published for the first time."

Recenzje

"The present volume is dedicated to the memory of Philippe Bénilan and contains about forty research articles which all previously appeared in the Journal of Evolution Equations. The topics covered are from Hamilton--Jacobi equations, the porous medium equation, reaction diffusion systems, integro-differential equations and viscoelasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein--Uhlenbeck operator." (Monatshefle für Mathematik, G. Teschl, Wien)

Spis treści

Intrinsic metrics and Lipschitz functions.- Decay estimates for “anisotropic” viscous Hamilton-Jacobi equationsin RN.- The Cauchy problem for linear growth functionals.- Asymptotic behaviour for the porous medium equation posedin the whole space.- Dirichlet and Neumann boundary conditions: What is in between?.- The focusing problem for the Eikonal equation.- Weak solutions and supersolutions in L1 for reaction-diffusion systems.- Global well-posedness and stability of a partial integro-differentialequation with applications to viscoelasticity.- On some singular limits of homogeneous semigroups.- Singular limit of changing sign solutions of the porous mediumequation.- On the regularizing effect of strongly increasing lower order terms.- Global smooth solutions for a quasilinear fractional evolution equation.- On the uniqueness of solutions for nonlinear elliptic-parabolicequations.- Conservation laws with discontinuous flux functions and boundary condition.- Regularity of solutions of nonlinear Volterra equations.- Nonautonomous heat equations with generalized Wentzellboundary conditions.- Maximal LP-regularity for elliptic operators with VMO-coefficients.- Linearized stability for nonlinear evolution equations.- D. Bothe Nonlinear evolutions with Carathéodory forcing.- Linear parabolic equations with singular potentials.- Some noncoercive parabolic equations with lower order termsin divergence form.- E. Feireisl On the motion of rigid bodies in a viscous incompressible fluid.- Minimization problems for eigenvalues of the Laplacian.- Rate of decay to equilibrium in some semilinear parabolic equations.- A new regularity result for Ornstein– Uhlenbeck generatorsand applications.- Global solution and smoothing effect for a non-local regularizationof a hyperbolic equation.- Convergence to equilibrium for a parabolic problem with mixedboundary conditions in one space dimension.- Analyticity of solutions to fully nonlinear parabolic evolutionequations on symmetric spaces.- Pointwise gradient estimates of solutions to onedimensionalnonlinear parabolic equations.- Uniqueness of entropy solutions for nonlinear degenerate parabolic problems.- Oscillatory boundary conditions for acoustic wave equations.- Existence and uniqueness results for large solutions of generalnonlinear elliptic equations.- Another way to say caloric.- Nonlinear problems related to the Thomas-Fermi equation.- Existence of attractors in L¡ã0(fi) for a class of reaction-diffusionsystems.- Uniqueness for an elliptic-parabolic problem with Neumannboundary condition.

O autorze

Wolfgang Arendt ist Professor für Analysis an der Universität Ulm. Sein Forschungsgebiet sind Funktionalanalysis und Partielle Differenzialgleichungen.