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The Final Solution (die Endlösung, diː ˈʔɛntˌløːzʊŋ) or the Final Solution to the Jewish Question (Endlösung der Judenfrage, ˈɛntˌløːzʊŋ deːɐ̯ ˈjuːdn̩ˌfʁaːɡə) was a Nazi plan for the genocide of individuals they defined as Jews during World War II. The "Final Solution to the Jewish question" was the official code name for the murder of all Jews within reach, which was not restricted to the European continent. This policy of deliberate and systematic genocide starting across German-occupied Europe was formulated in procedural and geopolitical terms by Nazi leadership in January 1942 at the Wannsee Conference held near Berlin, and culminated in the Holocaust, which saw the murder of 90% of Polish Jews, and two-thirds of the Jewish population of Europe. The Final Solution did not, however, include the hundreds of thousands of Jews killed by Romanian forces. By far the greatest extermination of Jews by non-German forces, this genocide was "operationally separate from the Nazi Final Solution". The nature and timing of the decisions that led to the Final Solution is an intensely researched and debated aspect of the Holocaust. The program evolved during the first 25 months of war leading to the attempt at "murdering every last Jew in the German grasp". Christopher Browning, a historian specializing in the Holocaust, wrote that most historians agree that the Final Solution cannot be attributed to a single decision made at one particular point in time. "It is generally accepted the decision-making process was prolonged and incremental." In 1940, following the Fall of France, Adolf Eichmann devised the Madagascar Plan to move Europe's Jewish population to the French colony, but the plan was abandoned for logistical reasons, mainly a naval blockade. There were also preliminary plans to deport Jews to Palestine and Siberia. In 1941, Raul Hilberg wrote that in the first phase of the mass-murder of Jews, the mobile killing units began to pursue their victims across occupied eastern territories; in the second phase, stretching across all of German-occupied Europe, the Jewish victims were sent on death trains to centralized extermination camps built for the purpose of systematic murder of Jews.

Stable blow up dynamics for energy supercritical wave equations

Roland Donninger

We study the semilinear wave equation

\displaystyle \partial _t^2 \psi -\Delta \psi =\vert\psi \vert^{p-1}\psi

for

p > 3

with radial data in three spatial dimensions. There exists an explicit solution which blows up at

t=T>0

given by $\displaystyl ...

American Mathematical Society2014