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.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes
The continuity and boundedness of the stress to the solution of the thermoelastic system is studied first for the linear case on a strip and then for the twodimensional model involving nonlinearities, noncontinuous heating regimes and isolated boundary nonsmoothnesses of the heated body.
On the regularity of the blow-up set for semilinear heat equations
On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property
On the solution of inverse problems for generalized oxygen consumption
We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.
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 stability of solutions of impulsive nonlinear parabolic equations
On the stability of solutions of impulsive nonlinear parabolic equations
Stability and asymptotic stability of the solutions of impulsive nonlinear pa ra bo lic equations are studied via the method of differential inequalities.
On the structure of the solution set of evolution inclusions with Fréchet subdifferentials.
On the structure of the solution set of evolution inclusions with time-dependent subdifferentials.
On the structure of the solution set of evolution inclusions with time-dependent subdifferentials
On the temperature distribution in cold ice
The linear heat equation predicts that the variations of temperature along a cold ice sheet {i.e. at a temperature less than is freezing point) due to a sudden increase in air temperature, are very very slow. Based on this we represent the nonlinear evolution of an ice sheet as a sequence of steady states. As a first fundamental indication that this model is correct well posedness with respect to the variations of initial and boundary data is proved. Further an estimate of the error made in evaluating...
On the time periodic free boundary associated to some nonlinear parabolic equations.