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nonlinear heat equation; Lamé system; noncontinuous heating regime; isolated boundary nonsmoothness; boundedness and continuity of the stresses; Sobolev spaces; Fourier transformation; temperature shock; quasi-linear thermoelasticity; homogeneous isotropic body; radiation term; stress field
The continuity and boundedness of the stress to the solution of the thermoelastic system is studied first for the linear case on a strip and then for the twodimensional model involving nonlinearities, noncontinuous heating regimes and isolated boundary nonsmoothnesses of the heated body.
[1] S. Agmon A. Douglis L. Nirenberg: Estimates near boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Part II. Comm. Pure Appl. Math. 17 (1964) 35-92. DOI 10.1002/cpa.3160170104 | MR 0162050
[2] O. V. Běsov V. P. lljin S. M. Nikolskij: Integral Transformations of Functions and Imbedding Theorems. (in Russian). Nauka, Moskva 1975.
[3] P. Grisvard: Elliptic Problems in Nonsmooth Domains. Monographs and Studies in Math. 24, Pitman, Boston-London-Melbourne 1985. MR 0775683 | Zbl 0695.35060
[4] P. Grisvard: Problemes aux limites dans les polygones, Mode d'emploi. EDF Bull. Direct. Etud. Rech. Ser. C. Math. Inform. (1986) 1, 21 - 59. MR 0840970 | Zbl 0623.35031
[5] J. Jarušek: Contact problems with bounded friction. Coercive case. Czech. Math. J. 33 (108) (1983), 237-261. MR 0699024
[6] J. Jarušek: Remark to the generalized gradient method for the optimal large-scale heating problem. Probl. Control Inform. Theory 16 (1987) 2, 89-99. MR 0907452
[7] J. Jarušek: Optimal control of thermoelastic processes III. (in Czech). Techn. rep. Inst. Inform. Th. Autom. No. 1561, Praha 1988.
[8] V. A. Kondratěv: Elliptic boundary value problems with conical or angular points. (in Russian). Trudy Mosk. Mat. Obšč., Vol. 16 (1967), 209-292. MR 0226187
[9] A. Kufner O. John S. Fučík: Function Spaces. Academia, Praha 1977. MR 0482102
[10] A. Kufner A. M. Sändig: Some Applications of Weighted Sobolev Spaces. Teubner-Texte Math., Band 100, Teubner V., Leipzig 1987. MR 0926688
[11] O. A. Ladyženskaja V. A. Solonnikov N. N. Uralceva: Linear and Quasilinear Equations of Parabolic Type. (in Russian). Nauka, Moskva 1967. MR 0241822
[12] J. L. Lions E. Magenes: Problèmes aux limites non-homogènes et applications. Dunod, Paris 1968.
[13] J. Nečas: Solution of the biharmonic problem for an infinite angle. (in Czech). Časopis pěst. mat. 83 (1958), Part I, 257-286, Part. II, 399-424.
[14] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha 1967. MR 0227584
[15] J. Nečas: Introduction to the Theory of Nonlinear Elliptic Equations. Teubner-Texte Math., Band 52, Teubner V., Leipzig 1983. MR 0731261
[16] R. H. Nochetto: Error estimates for two-phases Stefan problem in several space variables. Part II: Nonlinear flux conditions. Preprint No. 416, 1st. Anal. Numer, CNR. Pavia, Pavia 1984. MR 0775859
[17] A. M. Sändig U. Richter R. Sändig: The regularity of boundary value problems for the Lame equations in polygonal domain. Rostock. Math. Kolloq. 36 (1989), 21-50. MR 1006837
[18] A. Visintin: Sur le problème de Stefan avec flux non-lineaire. Preprint No. 230, Ist. Anal. Numer. C. N. R. Pavia, Pavia 1981. MR 0631569 | Zbl 0478.35084
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