On strong solutions of a Robin problem modelling heat conduction in materials with corroded boundary |
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Authors: | Rishad Shahmurov |
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Institution: | Department of Mathematics, University of Alabama, Tuscaloosa, USA Vocational High School, Okan University, Istanbul 34959, Turkey |
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Abstract: | Motivated by a practical problem on a corrosion process, we shall study a third kind of BVP for a large class of elliptic equations in vector-valued Lp spaces. Particularly we will determine optimal spaces for boundary data and get maximal regularity for inhomogeneous equations. Then based on these results we shall treat some nonlinear problems. Our approach will be based on the semigroup theory, the interpolation theory of Banach spaces, fractional powers of positive operators, operator-valued Fourier multiplier theorems and the Banach fixed point theorem. |
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Keywords: | Differential-operator equations Robin problem Interpolation of Banach spaces Semigroup estimates Operator-valued Fourier multipliers |
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