Initial-boundary value problems are considered for homogeneous parabolic systems with Dini-continuous coefficients and zero initial conditions in a semibounded plane domain with a nonsmooth lateral ...boundary admitting cusps, on which general boundary conditions with variable coefficients are given. A theorem on unique classical solvability of these problems in the space of functions that are continuous and bounded together with their first spatial derivatives in the closure of the domain is proved by applying the boundary integral equation method. A representation of the resulting solutions in the form of vector single-layer potentials is given.
We consider initial–boundary value problems for homogeneous parabolic systems with coefficients satisfying the double Dini condition with zero initial conditions in a semibounded plane domain with ...nonsmooth lateral boundary. The method of boundary integral equations is used to prove a theorem on the unique classical solvability of such problems in the space of functions that are continuous together with their first spatial derivative in the closure of the domain. An integral representation of the obtained solutions is given. It is shown that the condition for the solvability of the posed problems considered in the paper is equivalent to the well-known complementarity condition.
We prove the existence of a classical solution of the contact problem for Petrovskii parabolic systems of the second order with Dini continuous coefficients in a strip separated into two domains by a ...nonsmooth curve.
We consider the first and second initial–boundary value problems for inhomogeneous second-order parabolic systems with Dini continuous coefficients under nonzero initial conditions in bounded domains ...on the plane with nonsmooth lateral boundaries that, in particular, admit cusps. Theorems are proved on the unique classical solvability of these problems in the space of functions that are continuous together with their first spatial derivatives in the closure of these domains.
We consider the first initial–boundary value problem for a parabolic system in a semibounded domain on the plane with nonsmooth lateral boundary that may have cusps. The continuity of the trace of ...the Poisson potential on such a boundary is studied, and a theorem on the existence of a classical solution of the problem is proved for the case of an inhomogeneous parabolic system and a nonzero initial condition.
We consider the first initial–boundary value problem for a spatially one-dimensional second-order Petrovskii parabolic system with differentiable coefficients in a half-strip with nonsmooth lateral ...boundary. A theorem on the uniqueness of the classical solution of this problem is proved.
The first and second initial-boundary value problems for second-order parabolic systems with coefficients satisfying the Dini condition in a semibounded plane domain with a nonsmooth lateral boundary ...admitting cusps are considered. Theorems on the uniqueness of classical solutions of these problems in the class of functions that are continuous and bounded together with their first spatial derivatives in the closure of this domain are proved.
The first and second initial-boundary value problems for Petrovskii parabolic systems of the second order with coefficients satisfying the Dini condition in plane domains with nonsmooth lateral ...boundaries admitting, in particular, cusps are considered. Theorems on the uniqueness of classical solutions of these problems in the class of functions that are continuous and bounded together with their first spatial derivatives in the closure of these domains are proved.
We prove the existence of a classical solution of the contact problem for Petrovskii parabolic systems of the second order with Dini continuous coefficients in a strip separated into two domains by a ...nonsmooth curve.
One step, simple and environmentally friendly enzymatic synthesis of optically active polyaniline in the bulk solution and on the surface of glass slides (
in situ deposition) was developed. Fungal ...laccase from
Trametes hirsuta was used as the catalyst of the oxidative polymerisation of aniline. The reaction was carried out under aerobic condition in the weak acidic aqueous solution in the presence of the chiral dopant, such as (
S)- or (
R)-camphorsulfonic acid. The doping/de-doping procedure of optically active polyaniline was reversible. It was shown that a chiral conformation of the polyaniline was quite variable, and the optical activity of the polymer could be changed by the replacement of camphorsulfonic acid enantiomer in the polyaniline structure.
