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On a certain case of thermoelastic interaction of an opening and a heat spot of elliptic shape. (English. Russian original) Zbl 0882.73082
Phys.-Dokl. 40, No. 3, 142-145 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 341, No. 2, 194-197 (1995).
Using complex potentials, the authors solve an elastic plane problem as the following boundary value problem. Given a Hölder continuous function $$f(t)$$ on an ellipse $$L$$. Find the functions $$\varphi$$ and $$\psi$$ analytic in $$D^+$$ and $$D_-$$, respectively, where $$D^+$$ is the interior domain to $$L$$, $$D^-$$ is the exterior domain to $$L$$, with the boundary condition $$\varphi(t)+t \overline{\varphi'(t)}+ \overline{\psi(t)}= f(t)$$, $$t\in \ell\subset L$$, and with given jumps of $$\varphi$$ and $$\psi$$ on $$L\setminus \ell$$.
##### MSC:
 74S30 Other numerical methods in solid mechanics (MSC2010) 74B99 Elastic materials 30E25 Boundary value problems in the complex plane 80A20 Heat and mass transfer, heat flow (MSC2010)