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Examples of Fundamental Solutions
2017When the number \(n \ge 4\) of independent variables is even, the exponent m defined in Eq. ( 17.3.2) is a positive integer and the construction of U in Sect. 17.4 no longer holds, because the whole algorithm (see Eq. ( 17.4.4)) involves division by \((l-m)\), which vanishes when \(l=m\).
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The Concept of a Fundamental Solution
2013The first explicit encounter with the notion of fundamental solution takes place in this chapter and the classical Malgrange-Ehrenpreis theorem is presented.
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A Choice of Fundamental Solutions
1984A key ingredient in the formulation of boundary integral equations via the direct method is the so called “fundamental solution”. This is generally obtained as the particular singular solution of an elliptic boundary value problem which corresponds to a “concentrated load” (i.e.
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Fundamentals of Solution Growth
1989In order for growth to occur the solute species must move from the bulk solution to the crystal surface, be adsorbed on the crystal surface, move to a step, and finally move to a kink on the step. If ionic species are involved then dehydration and chemical reaction may also be required.
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Positivity of the fundamental solution for fractional diffusion and wave equations
Mathematical Methods in the Applied Sciences, 2021Jukka Kemppainen
exaly