On a familiy of torsional creep problems.
On a mathematical model for the crystallization of polymers
We consider a mathematical model proposed in [1] for the cristallization of polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. The model includes a constraint on the crystal volume fraction. Essentially, the model is a system of both second order and first order evolutionary partial differential equations with nonlinear terms which are Lipschitz continuous, as in [1], or Hölder continuous, as in [3]. The main novelty here is the...
On a mixed boundary values problem for Lavrentev type equations
On an over-determined problem of free boundary of a degenerate parabolic equation
This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants and , to decide the initial value such that the solution satisfies , where . In this paper, we first establish a priori estimate and a more precise Poincaré type inequality...
On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator.
On Lipschitz continuity of the solution map for two-dimensional wave maps
On nonlinear Schrödinger equations
On positive solutions for a class of strongly coupled -Laplacian systems.
On pseudosymmetric hyperbolic systems
On stability and growth of solutions for classes of initial and boundary value problems
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 complex structure of positive solutions to Matukuma-type equations
On the domain dependence of solutions to the two-phase Stefan problem
We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains converge to a solution of the same problem on a domain where is the limit of in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on .
On the effect of the domain geometry on uniqueness of positive solutions of
On the existence of positive solution for an elliptic equation of Kirchhoff type via Moser iteration method.
On the existence of solutions of some non-linear Dirichlet problems
On the global regularity of subcritical Euler–Poisson equations with pressure
We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual -law pressure, , admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the -system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann...
On the hyperbolic Dirichlet to Neumann functional.
On the influence of domain shape on the existence of large solutions of some superlinear problems.
On the local and global well-posedness theory for the KP-I equation