On the iterated Green functions on a bounded domain and their related Kato class of potentials.
On the jump set of solutions of the total variation flow
On the Korteweg-De Vries Equation.
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 lack of null-controllability of the heat equation on the half space.
On the least principal fundamental solution of a parabolic differential equation
On the linear and quasilinear parabolic equations
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 a class of autonomous reaction-diffusion 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 Numerical Errors in One Step Algorithms for Time Dependent Problems.
On the Numerical Integration of the Heat Equation.
On the numerical solution of the diffusion equation with a nonlocal boundary condition.
On the numerical solution of the one-dimensional convection-diffusion equation.
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 parabolic potentials in degenerate-type heat equation.