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Distributions and Fundamental Solutions
2015This chapter is an introduction to distribution theory illustrated by the verification of fundamental solutions of the classical operators \(\Delta _{n}^{k},(\lambda -\Delta _{n})^{k},(\Delta _{n}+\lambda )^{k},\partial _{\bar{z}}, (\partial _{t}^{2} - \Delta _{n})^{k},\partial _{1}\cdots \partial _{k},(\partial _{t} -\lambda \Delta _{n})^{k},(\partial
Norbert Ortner, Peter Wagner
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A Note on fundamental solutions
Communications in Partial Differential Equations, 1999(1999). A Note on fundamental solutions. Communications in Partial Differential Equations: Vol. 24, No. 1-2, pp. 369-376.
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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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Fundamental Equations and Solutions
2009Every other day one may observe puzzling fluid mechanics phenomena. Such counter-intuitive examples include: (a) Keeping the tailgate of a pick-up truck up reduces aerodynamic drag (why?) and hence saves gasoline; although, most drivers intentionally keep it down and even install “airflow” nets to retain cargo when accelerating.
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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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