Gain of regularity for equations of KdV type
Galerkin approximations for nonlinear evolution inclusions
In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.
Galerkin approximations to non-linear pseudo-parabolic partial differential equations. (Short Communication).
Galerkin approximations to non-linear pseudo-parabolic partial differential equations.
Galerkin methods for nonlinear Sobolev equations.
Galerkin Methods for Parabolic Equations with Nonlinear Boundary Conditions.
Galerkin time-stepping methods for nonlinear parabolic equations
We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.
Galerkin time-stepping methods for nonlinear parabolic equations
We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.
Game-theoretic schemes for generalized curvature flows in the plane.
Gas-solid reaction with porosity change.
Gauss' hypergeometric series and heat production in a cylinder
Gaussian Bounds for the Fundamental Solutions ...
Gaussian estimates for fundamental solutions to certain parabolic systems.
Auscher proved Gaussian upper bound estimates for the fundamental solutions to parabolic equations with complex coefficients in the case when coefficients are time-independent and a small perturbation of real coefficients. We prove the equivalence between the local boundedness property of solutions to a parabolic system and a Gaussian upper bound for its fundamental matrix. As a consequence, we extend Auscher's result to the time dependent case.
Gaussian lower bounds for random walks from elliptic regularity
General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations
New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.
General finite difference approximation to the Cauchy problem for nonlinear parabolic differential-functional equations
Generalized Fokker-Planck equations and convergence to their equilibria
We consider extensions of the classical Fokker-Planck equation uₜ + ℒu = ∇·(u∇V(x)) on with ℒ = -Δ and V(x) = 1/2|x|², where ℒ is a general operator describing the diffusion and V is a suitable potential.
Generalized Functions Solutions of Monotone and Semilinear Parabolic Equations.
Generation of analytic semi-groups in L2 for a class of second order degenerate elliptic operators
Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion
In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.