On the differential system governing flows in magnetic field with data in .
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 solutions of nonlinear infinite systems of parabolic differential-functional equations.
On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures.
On the finite dimension of attractors of doubly nonlinear parabolic systems with l-trajectories
This paper is concerned with the asymptotic behaviour of a class of doubly nonlinear parabolic systems. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.
On the Fourier's first problem for a system of non-linear parabolic equations with unbounded coefficients
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 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 interior differentiability of weak solutions of parabolic systems with quadratic growth nonlinearities
On the jump set of solutions of the total variation flow
On the Kuramoto-Sivashinsky equation in a disk
We consider the first initial-boundary value problem for the 2-D Kuramoto-Sivashinsky equation in a unit disk with homogeneous boundary conditions, periodicity conditions in the angle, and small initial data. Apart from proving the existence and uniqueness of a global in time solution, we construct it in the form of a series in a small parameter present in the initial conditions. In the stable case we also obtain the uniform in space long-time asymptotic expansion of the constructed solution and...
On the local behaviour of solutions of a certain class of doubly nonlinear parabolic equations.
On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients
On the local integrability and boundedness of solutions to quasilinear parabolic systems.
On the long-time behaviour of solutions of the p-Laplacian parabolic system
Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be , and in the variable exponent case, L² and -weak.
On the method of lines for a non-linear heat equation with functional dependence
We consider a heat equation with a non-linear right-hand side which depends on certain Volterra-type functionals. We study the problem of existence and convergence for the method of lines by means of semi-discrete inverse formulae.
On the Neumann Problem for the Nonlinear Parabolic Equation of Eells-Sampson and Harmonie Mappings.
On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.
On the properties of the solution set of nonconvex evolution inclusions of the subdifferential type
In this paper we consider nonconvex evolution inclusions driven by time dependent convex subdifferentials. First we establish the existence of a continuous selection for the solution multifunction and then we use that selection to show that the solution set is path connected. Two examples are also presented.