On principal eigenvalues for periodic parabolic Steklov problems.
On solutions of a perturbed fast diffusion equation
The paper concerns the (local and global) existence, nonexistence, uniqueness and some properties of nonnegative solutions of a nonlinear density dependent diffusion equation with homogeneous Dirichlet boundary conditions.
On some stochastic parabolic differential equations in a Hilbert space.
On step-like contrast structure of singularly perturbed systems.
On the antimaximum principle for parabolic periodic problems with weight.
On the asymptotic behavior of solutions of linear parabolic equations in space
On the asymptotic behavior of solutions of parabolic equations
On the boundary value problem for the spectrally loaded heat conduction operator.
On the Convergence of Finite-Difference Schemes for Parabolic Equations with Variable Coefficients.
On the eigenfunction expansion method for semilinear dissipative equations in bounded domains and the Kuramoto-Sivashinsky equation in a ball
Presented herein is a method of constructing solutions of semilinear dissipative evolution equations in bounded domains. For small initial data this approach permits one to represent the solution in the form of an eigenfunction expansion series and to calculate the higher-order long-time asymptotics. It is applied to the spatially 3D Kuramoto-Sivashinsky equation in the unit ball B in the linearly stable case. A global-in-time mild solution is constructed in the space , s < 2, and the uniqueness...
On the existence of positive solutions for periodic parabolic sublinear problems.
On the oscillation of some impulsive parabolic equations with several delays
In this paper, several oscillation criteria are established for some nonlinear impulsive functional parabolic equations with several delays subject to boundary conditions. We shall mainly use the divergence theorem and some corresponding impulsive delayed differential inequalities.
On the solution of the heat equation with nonlinear unbounded memory
The paper deals with the question of global solution to boundary value problem for the system of semilinear heat equation for and complementary nonlinear differential equation for (“thermal memory”). Uniqueness of the solution is shown and the method of successive approximations is used for the proof of existence of a global solution provided the condition holds. The condition is verified for some particular cases (e. g.: bounded nonlinearity, homogeneous Neumann problem (even for unbounded...
On the solutions of nonlinear initial-boundary value problems.
On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces.
On the solvability of parabolic and hyperbolic problems with a boundary integral condition.
On the Stefan problem with energy specification
Vengono trattati due problemi di Stefan con la specificazione dell'energia. Dapprima si fornisce una formulazione debole di un problema unidimensionale ad una fase studiato in [4]: si dimostra un risultato di esistenza. In seguito si considera un problema di Stefan pluridimensionale e multifase in cui viene assegnata l'energia totale del sistema ad ogni istante; si mostra l’esistenza e l’unicità della soluzione per due formulazioni provando inoltre l’equivalenza fra queste.
On the volume of intersection of three independent Wiener sausages
Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.
On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification.
On the well-posedness of the heat equation on unbounded domains.