Solutions to semilinear parabolic equations driven by mixed local-nonlocal operators blow up in finite time for sufficiently large initial data, for reaction terms like u^p with any p>1.
Levine,The role of critical exponents in blowup theorems, SIAM Rev.32, (1990), 262–288
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Blow-up of solutions to semilinear parabolic equations driven by mixed local-nonlocal operators with large initial data
Solutions to semilinear parabolic equations driven by mixed local-nonlocal operators blow up in finite time for sufficiently large initial data, for reaction terms like u^p with any p>1.