The variation of the Hall coefficient and the electrical conductivity under hydrostatic pressure up to 10 katm and in the temperature range from 77 to 300 K was measured in mixed crystals of MnkHgl -kTe ( k < 0.10). From the analysis of the pressure and temperature dependences of the electron concentration the energy gap E, = E(r,) -E(l?,) was determined for k = 0.012; 0.05; 0.07; and 0.09 in the temperature interval from 77 t o 300 K. If is found, that the energy gap dependence is linear with composition within the investigated range of composition. It is established, that a = dE,/dT and y = dE,/dp are positive and equal 5 x eV/atm, respectively. This is the first attempt to determine the dependence of the energy gap on the composition in Mn,Hgl-kTe mixed crystals for k < 0.10. The obtained results are quite similar to the energy dependence on composition in Cd,Hgl -,Te, but significant differences occur in quantitative values. I n iMnkHgl-kTe ( k < 0,lO)-Einkristallen wurde die Anderung des Hall-Koeffizienten und der elektrischen Leitfahigkeit bei hydrostatischem Druck bis zu 10 katm im Temperaturbereich von 77 bis 300 K untersucht. Ails der Analyse der Druck-und Temperaturabhangigkeit der Elektronenkonzentration wurde die Energielucke E, = E ( r , ) -E(r,) fur k = 0,012; 0,05; O,07; und 0,09 im Temperaturbereich von 77 bis 300 K bestimmt. Es wird gefunden, daB die Abhangigkeit der Energielucke linear von der Zusammensetzung im untersuchten Bereich abhangt. Es wird festgestellt, daB a = dE,/dT und y = dEo/dp positiv sind und Werte von 5 x lo-* eV/grd bzw. 9 x eV/atm besitzen. Dies stellt den ersten Versuch dar, die Abhangigkeit der Energielucke von der Zusammensetziing in MnkHgl -kTe-Mischkristallen fur k < 0,lO zu bestimmen. Die erhaltenen Ergebnisse sind der Energieabhangigkeit in Cd,Hgl -,Te ahnlich, jedoch treten bedeutende Unterschiede bei den quantitativen GrbBen auf.

SUMMARYThe existence of global-in-time weak solutions to the Joule problem modelling heating or cooling in a current and heat conductive medium is proved via the Faedo -Galerkin method. The existence proof entails some a priori estimates that together with the monotonicity and compactness methods make up a main tool to prove the desired result. Under appropriate hypotheses on the data, it will be shown the boundedness in L∞(Q T ) of the absolute temperature of the medium and of the t-derivative of this temperature, which is achieved by means of the Gagliardo -Nirenberg theorem, the Sobolev embedding theorem and the method of Stampacchia. The paper is some extension of our investigation initiated in (Math. Meth. Appl. Sci. 1998; 23:1275-1291 PRELIMINARIES AND STATEMENT OF THE RESULTThe main aim of this paper is to prove existence of global-in-time weak solutions to the initial-boundary value problem describing Joule's heating in a heat and current conductive medium in three space dimensions; this problem reads:

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