On the , and - version of the finite element method
On the Heat Equation and the Index Theorem.
On the heat kernel and the Korteweg--de Vries hierarchy
We give explicit formulas for Hadamard's coefficients in terms of the tau-function of the Korteweg-de Vries hierarchy. We show that some of the basic properties of these coefficients can be easily derived from these formulas.
On the heat trace of the magnetic Schrödinger operators on the hyperbolic plane.
On the Hénon equation : asymptotic profile of ground states, I
On the hierarchies of higher order mKdV and KdV equations
The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces defined by the norm . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ . The proof uses an appropriate variant of the Fourier restriction norm method. A counterexample is discussed to show that the Cauchy problem for equations of this type is in general ill-posed in the C 0-uniform sense, if s < . The results for r = 2 - so far in...
On the Hölder Continuity of Bounded Weak Solutions of Quasilinear Parabolic Systems.
On the Hölder continuity of solutions of nonlinear parabolic systems
Non-linear second order parabolic systems in the divergent form are considered. It is proved that under some restrictions on the modulus of ellipticity, all weak solutions are continuous.
On the Hölder continuity of solutions of second order elliptic equations in two variables
On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order
On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions
We prove the interior Hölder continuity of weak solutions to parabolic systems (), where the coefficients are measurable in , Hölder continuous in and Lipschitz continuous in and .
On the Hölder-continuity of solutions of a nonlinear parabolic variational inequality
On the homogenization of problems in the theory of elasticity on composite structures.
On the homogenization of some nonlinear problems in perforated domains
On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary
In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].
On the hyperbolic Dirichlet to Neumann functional.
On the hyperbolic linear functional equations.
On the hyperbolicity of a third order operator and the generalized Goursat-Darboux problem
On the hypoellipticity of pseudo-differential systems with a diagonal principal symbol
On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials
We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well-known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the...