𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a contact problem for a system of parabolic equations in the thermal conductivity of electric machines: II

✍ Scribed by Romuald Małecki; Paweł Olszewski; Jacek Urbanowicz; Wojciech Urbański

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
489 KB
Volume
13
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The non‐linear contact problem for the parabolic system of second order in the sense of Pietrovski, which is the generalization of the problem considered in Part I (preceding paper), is formulated. The matrix of fundamental solutions for parabolic systems of second order with coefficients containing unknown functions and their first‐order derivatives is constructed and used to reduce the problem to the equivalent system of integral equations which is then reduced to a system of Volterra type of the second kind. The existence of the solution of the system obtained is proved by using the Schauder fixed‐point theorem.

📜 SIMILAR VOLUMES

A Remark on the Global Solvability of th
A Remark on the Global Solvability of the Cauchy Problem for Quasilinear Parabolic Equations
✍ Aris S. Tersenov 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 81 KB

The present paper is concerned with the global solvability of the Cauchy problem for the quasilinear parabolic equations with two independent variables: Ž . Ž . u s a t, x, u, u u q f t, x, u, u . We investigate the case of the arbitrary order < < of growth of the function f t, x, u, p with respect

Continuous dependence on the geometry an
Continuous dependence on the geometry and on the initial time for a class of parabolic problems II
✍ G. A. Philippin; V. Proytcheva 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 139 KB 👁 1 views

## Abstract Extending the investigations initiated in an earlier paper, the authors deal in this paper with the solutions of another class of initial‐boundary value problems for which continuous dependence inequalities on the geometry and the initial time are established. Copyright © 2007 John Wile

Critical Exponents for the Blowup of Sol
Critical Exponents for the Blowup of Solutions with Sign Changes in a Semilinear Parabolic Equation, II
✍ Noriko Mizoguchi; Eiji Yanagida 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 353 KB

The blowup of solutions of the Cauchy problem { u t =u xx + |u| p&1 u u(x, 0)=u 0 (x) in R\\_(0, ), in R is studied. Let 4 k be the set of functions on R which change sign k times. It is shown that for p k =1+2Â(k+1), k=0, 1, 2, ... , any solution with u 0 # 4 k blows up in finite time if 1 p k . T

An inverse coefficient problem for a par
An inverse coefficient problem for a parabolic equation in the case of nonlocal boundary and overdetermination conditions
✍ Mansur I. Ismailov; Fatma Kanca 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 174 KB 👁 1 views

## Communicated by A. Kirsch In this paper, the inverse problem of finding the time-dependent coefficient of heat capacity together with the solution of heat equation with nonlocal boundary and overdetermination conditions is considered. The existence, uniqueness and continuous dependence upon the

On a resolvent estimate of the Stokes sy
On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier–Stokes equations
✍ Y. Shibata; S. Shimizu 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 228 KB 👁 1 views

## Abstract In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fluid flow. We show standard resolvent estimates in the __L~q

On a generalization of the Neumann probl
On a generalization of the Neumann problem for the Laplace equation outside cuts in a plane
✍ P. A. Krutitskii; A. O. Chikilev; N. Ch. Krutitskaya; V. V. Kolybasova 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB 👁 1 views

## Abstract A boundary value problem for harmonic functions outside cuts in a plane is considered. The jump of the normal derivative is specified on the cuts as well as a linear combination of the normal derivative on one side of the cut and the jump of the unknown function. The problem is studied