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Nonexistence of global solutions for time fractional wave equations in an exterior domain. (English) Zbl 07714667

Summary: This paper concerns two classes of initial-boundary value problems of semilinear time fractional wave equations in an exterior domain. Based on a special technique of test functions, we determine some critical exponents in the sense of Fujita for a corresponding problem. We also obtain the existence and nonexistence of global weak solutions with certain appropriate conditions.

MSC:

35B44 Blow-up in context of PDEs
35B33 Critical exponents in context of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
35R11 Fractional partial differential equations
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References:

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