## Abstract The paper is concerned with initial‐boundary value problem in two‐dimensional (2‐D) non‐linear thermoelasticity which arises as a mathematical model of shape memory alloys. The problem has the form of viscoelasticity system with fourth order capillarity‐like term coupled with heat condu
Blow-up in non-linear three-dimensional thermoelasticity
✍ Scribed by Reinhard Racke
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 270 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
It is shown that solutions of the equations of thermoelasticity in general will develop singularities in finite time.
📜 SIMILAR VOLUMES
0010-13640/81/00344029S2.30 'I$ need not even be defined for all arguments, since u' and u" will stay small for sufficiently small norms off, g. 2Solutions of the one-dimensional problem (4a, b) can also be viewed as special solutions u(x.r) of the n-dimensional equation u,, = c(u,,)Au which happen
In this paper, we consider a one-dimensional non-linear system of thermoelasticity with second sound. We establish an exponential decay result for solutions with small 'enough' initial data. This work extends the result of Racke (Math. Methods Appl. Sci. 2002; 25:409 -441) to a more general situatio
## Abstract In this paper the degenerate parabolic system __u__~__t__~=__u__(__u__~__xx__~+__av__). __vt__=__v__(__v__~__xx__~+__bu__) with Dirichlet boundary condition is studied. For $a. b {<} \lambda\_{1} (\sqrt {ab} {<} \lambda\_{1} {\rm if}\, \alpha\_{1} {\neq} \alpha\_{2})$, the global existe