On the existence of solutions and one-step method for functional-differential equations with parameters
On the existence of solutions of nonlinear infinite systems of parabolic differential-functional equations.
On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients
On the existence of weak solutions of boundary value problems in a diffusion model for an inhomogeneous liquid in regions with moving boundaries
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 Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion
Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological phenomena. This paper begins with a survey of applications to ecology, cell biology and bacterial colony patterns. The author then reviews mathematical results on the existence of travelling wave front solutions of these equations, and their generation from given initial data. A detailed study is then presented of the form of smooth-front...
On the Fourier's first problem for a system of non-linear parabolic equations with unbounded coefficients
On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order
We are concerned with the problem of differentiability of the derivatives of order of solutions to the “nonlinear basic systems” of the type We are able to show that for and this result suggests that more regularity is not expectable.
On the frictionless unilateral contact of two viscoelastic bodies.
On the function and the heat equation
On the global attractors for a class of semilinear degenerate parabolic equations
We prove the existence and upper semicontinuity with respect to the nonlinearity and the diffusion coefficient of global attractors for a class of semilinear degenerate parabolic equations in an arbitrary domain.
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 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 Hölder-continuity of solutions of a nonlinear parabolic variational inequality
On the initial-boundary value problems for a degenerate parabolic equation
For an equation of the type of porous media equation the Cauchy-Dirichlet and Cauchy-Neumann problems are considered. The existence and uniqueness results in the case of initial and boundary data are given.
On the interior differentiability of weak solutions of parabolic systems with quadratic growth nonlinearities