On the asymptotics of the spectrum of a thin plate problem of elasticity.
On the Asypmptotic Behaviour of Solutions of Nonlinear Parabolic Equations.
On the behavior of a nonstationary Poiseuille solution as .
On the behavior of solutions of parbolic equations with unbounded coefficients
On the behaviour of generalized solutions to genuinely nonlinear first order equations for small and large values of time.
The paper deals with the asymptotic behavior of generalized solutions to nonlinear first order equations. With the aid of explicit variational representation one studies the decrease of solutions for a large time. And for the small time an asymptotic of the perturbation?s front is calculated.
On the behaviour of solutions to the nonlinear elliptic Neumann problem in unbounded domains
The asymptotic behaviour is studied for minima of regular variational problems with Neumann boundary conditions on noncompact part of boundary.
On the blow up criterion for the 2-D compressible Navier-Stokes equations
Motivated by [10], we prove that the upper bound of the density function controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.
On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D
On the blowing up of solutions to nonlinear wave equations in two space dimensions.
On the blowup of multidimensional semilinear heat equations
On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴
We characterize the dynamics of the finite time blow-up solutions with minimal mass for the focusing mass-critical Hartree equation with H¹(ℝ⁴) data and L²(ℝ⁴) data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we analyze the mass concentration phenomenon of such blow-up solutions.
On the blow-up set for non-Newtonian equation with a nonlinear boundary condition.
On the blowup theory for the critical nonlinear Schrödinger equations
On the boundary conditions at the contact interface between a porous medium and a free fluid
On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions
On the boundedness of the mapping in Besov spaces
For , precise conditions on the parameters are given under which the particular superposition operator is a bounded map in the Besov space . The proofs rely on linear spline approximation theory.
On the Caginalp system with dynamic boundary conditions and singular potentials
This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in...
On the Cauchy problem for linear hyperbolic functional-differential equations
We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing...
On the Cauchy problem for the Yang-Mills field equations
On the Cauchy Problem in Nonlinear 3-d-Thermoelasticity.