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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T04:36:02Z","timestamp":1683261362164},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,4,25]],"date-time":"2023-04-25T00:00:00Z","timestamp":1682380800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,4,25]],"date-time":"2023-04-25T00:00:00Z","timestamp":1682380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100008678","name":"Universit\u00e4t Leipzig","doi-asserted-by":"crossref"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Calc. Var."],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give a sufficient condition for non-existence of global nonnegative mild solutions of the Cauchy problem for the semilinear heat equation <jats:inline-formula><jats:alternatives><jats:tex-math>$$u' = Lu + f(u)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mrow>\n <mml:msup>\n <mml:mi>u<\/mml:mi>\n <mml:mo>\u2032<\/mml:mo>\n <\/mml:msup>\n <mml:mo>=<\/mml:mo>\n <mml:mi>L<\/mml:mi>\n <mml:mi>u<\/mml:mi>\n <mml:mo>+<\/mml:mo>\n <mml:mi>f<\/mml:mi>\n <mml:mrow>\n <mml:mo>(<\/mml:mo>\n <mml:mi>u<\/mml:mi>\n <mml:mo>)<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> in <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^p(X, m)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mrow>\n <mml:msup>\n <mml:mi>L<\/mml:mi>\n <mml:mi>p<\/mml:mi>\n <\/mml:msup>\n <mml:mrow>\n <mml:mo>(<\/mml:mo>\n <mml:mi>X<\/mml:mi>\n <mml:mo>,<\/mml:mo>\n <mml:mi>m<\/mml:mi>\n <mml:mo>)<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for <jats:inline-formula><jats:alternatives><jats:tex-math>$$p \\in [1,\\infty )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mrow>\n <mml:mi>p<\/mml:mi>\n <mml:mo>\u2208<\/mml:mo>\n <mml:mo>[<\/mml:mo>\n <mml:mn>1<\/mml:mn>\n <mml:mo>,<\/mml:mo>\n <mml:mi>\u221e<\/mml:mi>\n <mml:mo>)<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where (<jats:italic>X<\/jats:italic>,\u00a0<jats:italic>m<\/jats:italic>) is a <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\sigma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mi>\u03c3<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-finite measure space, <jats:italic>L<\/jats:italic> is the infinitesimal generator of a sub-Markovian strongly continuous semigroup of bounded linear operators in <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^p(X, m)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mrow>\n <mml:msup>\n <mml:mi>L<\/mml:mi>\n <mml:
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