Abstract
We consider the nonlinear hyperbolic‐type inequality under the Dirichlet‐type boundary condition where , and . An optimal Fujita‐type result is obtained for this problem. Namely, we prove that when belongs to a certain functional space , and or , then there exists no global weak solution, while global solutions exist for some when and . The obtained result shows an interesting phenomenon of discontinuity of the Fujita critical exponent, jumping from to as reaches the value from above.
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