The generalized Burgers equation with and without a time delay.
The generalized Cauchy problem with data on two surfaces for a quasilinear analytic system.
The generalized Conley index and multiple solutions of semilinear elliptic problems.
The generalized Dirichlet problem for equations of Monge-Ampère type
The generalized Morawetz problem for Lavrent'ev-Bitsadze equation with spectral parameter.
The generalized Riemann-Hilbert boundary value problem for non-homogeneous polyanalytic differential equation of order in the Sobolev space .
The genuinely nonlinear Graetz-Nusselt ultraparabolic equation.
The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
The geometric theory of Volterra integral equations - a preliminary report
The geometrical quantity in damped wave equations on a square
The energy in a square membrane Ω subject to constant viscous damping on a subset decays exponentially in time as soon as ω satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate of this decay satisfies (see Lebeau [Math. Phys. Stud.19 (1996) 73–109]). Here denotes the spectral abscissa of the damped wave equation operator and is a number called the geometrical quantity of ω and defined as follows. A ray in Ω is the trajectory generated by the free motion...
The Geometry of Differential Harnack Estimates
In this short note, we hope to give a rapid induction for non-experts into the world of Differential Harnack inequalities, which have been so influential in geometric analysis and probability theory over the past few decades. At the coarsest level, these are often mysterious-looking inequalities that hold for ‘positive’ solutions of some parabolic PDE, and can be verified quickly by grinding out a computation and applying a maximum principle. In this note we emphasise the geometry behind the Harnack...
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem
The Global Cauchy Problem for the Non Linear Klein-Gordon Equation.
The global Cauchy problem for the non linear Klein-Gordon equation-II
The global Cauchy problem for the non linear Schrödinger equation revisited
The global existence of weak solutions of the mollified system of equations of motion of viscous compressible fluid
The global nonlinear stability of the Minkowski space
The global solubility of problems of nonlinear vibrations of plates on nonlinear foundations.
The global solvability to the equations of motion of viscous gas with an artificial viscosity