Hardy inequalities and dynamic instability of singular Yamabe metrics
Harnack inequalities for curvature flows depending on mean curvature.
Homogenization of periodic semilinear parabolic degenerate PDEs
Homotopy perturbation method for solving reaction-diffusion equations.
Improved least-squares error estimates for scalar hyperbolic problems.
Inéquations variationnelles d'évolution paraboliques du 2ème ordre
Inverse parabolic problems and discrete orthogonality.
Irregular boundary value problems for ordinary differential equations
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension
We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution , the graph of its blow-up points and the set of all characteristic points and show that is locally finite. Finally, given , we show that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least two) solitons, with alternate signs and that forms a...
Krylov subspace spectral methods for variable-coefficient initial-boundary value problems.
-convergence of finite element Galerkin approximations for parabolic problems
Lagrangian and moving mesh methods for the convection diffusion equation
We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington, SIAM J. Numer. Anal. 43 (2006) 2478–2499; Chrysafinos and Walkington, SIAM J. Numer. Anal. 44 (2006) 349–366] and the dependence of various constants upon the diffusion parameter is ...
Large time behavior of solutions to a class of doubly nonlinear parabolic equations
We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation with an initial condition . Here the exponents , and satisfy , and .
Large time behaviour in convection-diffusion equations
Large time behaviour of a class of solutions of second order conservation laws
% We study the large time behaviour of entropy solutions of the Cauchy problem for a possibly degenerate nonlinear diffusion equation with a nonlinear convection term. The initial function is assumed to have bounded total variation. We prove the convergence of the solution to the entropy solution of a Riemann problem for the corresponding first order conservation law.
Large time behaviour of solutions to nonhomogeneous diffusion equations
This note is devoted to the study of the long time behaviour of solutions to the heat and the porous medium equations in the presence of an external source term, using entropy methods and self-similar variables. Intermediate asymptotics and convergence results are shown using interpolation inequalities, Gagliardo-Nirenberg-Sobolev inequalities and Csiszár-Kullback type estimates.
Life span of nonnegative solutions to certain quasilinear parabolic Cauchy problems.
L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type
Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation...
Local Existence and Regularity for a Class of Degenerate Parabolic Equations.
Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions,...