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- W4383497804 abstract "This paper concerns autonomous boundary value problems for 1D semilinear hyperbolic PDEs. For time-periodic classical solutions, which satisfy a certain non-resonance condition, we show the following: If the PDEs are continuous with respect to the space variable x and C∞-smooth with respect to the unknown function u, then the solution is C∞-smooth with respect to the time variable t, and if the PDEs are C∞-smooth with respect to x and u, then the solution is C∞-smooth with respect to t and x. The same is true for appropriate weak solutions. Moreover, we show examples of time-periodic functions, which do not satisfy the non-resonance condition, such that they are weak, but not classical solutions, and such that they are classical solutions, but not C∞-smooth, neither with respect to t nor with respect to x, even if the PDEs are C∞-smooth with respect to x and u. For the proofs we use Fredholm solvability properties of linear time-periodic hyperbolic PDEs and a result of E. N. Dancer about regularity of solutions to abstract equivariant equations." @default.
- W4383497804 created "2023-07-08" @default.
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- W4383497804 date "2024-01-01" @default.
- W4383497804 modified "2023-10-16" @default.
- W4383497804 title "Regularity of time-periodic solutions to autonomous semilinear hyperbolic PDEs" @default.
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- W4383497804 doi "https://doi.org/10.1016/j.jmaa.2023.127562" @default.
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