藤原和将の論文
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論文
  1. K. Fujiwara and V. Georgiev, A new class of small initial data which may shift the critical power and lifespan estimates for the classical damped wave equations, to appear in Evol. Equ. Control Theory.
  2. K. Fujiwara, Note on the lifespan estimate of solutions for non-gauge invariant semilinear massless semirelativistic equations with some scaling critical nonlinearity, to appear in Journal of Evolution Equations. doi:10.1007/s00028-022-00865-9
  3. K. Fujiwara, Lifespan estimates of 1D non-gauge invariant semilinear semirelativistic equations,
    Applied Mathematics Letters, 124(2022), 107619, doi: 10.1016/j.aml.2021.107619, [Mathscinet: MR4307926].
  4. K. Fujiwara, Remark on the Chain rule of fractional derivative in the Sobolev framework,
    Math. Inequal. Appl., 24(2021), 1113--1124, doi: dx.doi.org/10.7153/mia-2021-24-77, [Mathscinet: MR4364567].
  5. K. Fujiwara, M. Ikeda, and Y. Wakasugi, The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping,
    Nonlinear Differ. Equ. Appl., 28(2021), Article Number:63, doi: 10.1007/s00030-021-00723-6, [bib:FuIkWa_2003_09239].
  6. K. Fujiwara and V. Georgiev, On global existence of $L^2$ solutions for 1D periodic NLS with quadratic nonlinearity,
    J. Math. Phys., 62(2021), 091504, doi:10.1063/5.0033101, [bib:FuGe_2009_04280].
  7. M. D'Abbicco and K. Fujiwara, A test function method for evolution equations with fractional powers of the Laplace operator,
    Nonlinear Analysis, 202(2021), 112114, doi: 10.1016/j.na.2020.112114, [Mathscinet: MR4145650].
  8. K. Fujiwara, V. Georgiev, and T. Ozawa, Self-similar solutions to the derivative nonlinear Schrodinger equation,
    J. Differential Equations, 268(2020), 7940--7961, doi: 10.1016/j.jde.2019.11.089 [Mathscinet: MR4079021].
  9. K. Fujiwara, V. Georgiev, and T. Ozawa, On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases,
    J. Math. Pures Appl., 136(2020), 239--256, doi: 10.1016/j.matpur.2019.10.003, [Mathscinet: MR4076963].
  10. K. Fujiwara, M. Ikeda, and Y. Wakasugi, Lifespan of solutions for a weakly coupled system of semilinear heat equations,
    Tokyo J. Math., 43 (2020), 163–-180, doi: 10.3836/tjm/1502179300, [Mathscinet: MR4121792].
  11. L. Forcella, K. Fujiwara, V. Georgiev, and T. Ozawa, Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential,
    Discrete Contin. Dyn. Syst., 39(2019), 2661--2678, doi: 10.3934/dcds.2019111, [Mathscinet: MR3927528].
  12. K. Fujiwara, Remark on the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity with mass,
    Pliska Stud. Math., 30(2019), 71--84. arXiv:1809.10202, [Mathscinet: MR3898132].
  13. K. Fujiwara, M. Ikeda, and Y. Wakasugi, Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity,
    Funkcial. Ekvac., 62(2019), 157--189, doi:https://doi.org/10.1619/fesi.62.157, [Mathscinet: MR3970099].
  14. K. Fujiwara, A note for the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity,
    Math. Meth. Appl. Sci., 41 (2018), 4955--4966, doi:10.1002/mma.4944, [Mathscinet: MR3843572].
  15. K. Fujiwara, V. Georgiev, and T. Ozawa, Blow-up for self-interacting fractional Ginzburg-Landau equation,
    Dyn. Partial Differ. Equ., 15 (2018), 175 -- 182. doi:10.4310/DPDE.2018.v15.n3.a1, [Mathscinet: MR3809638].
  16. K. Fujiwara, V. Georgiev, and T. Ozawa, Higher order fractional Leibniz rule,
    J. Fourier Anal. Appl. 24 (2018), 650--665, doi:10.1007/s00041-017-9541-y, [Mathscinet: MR3802288].
  17. K. Fujiwara and T. Ozawa, On the lifespan of strong solutions to the periodic derivative nonlinear Schr\"odinger equation,
    Evol. Equ. Control Theory, 7(2017), 275--280, doi:10.3934/eect.2018013, [Mathscinet: MR3809638].
  18. K. Fujiwara, M. Ikeda and Y. Wakasugi, Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations,
    Electron. J. Differential Equations, 2017 (2017), No. 196, 1-18, [Link], [Mathscinet: MR3690223].
  19. K. Fujiwara and T. Ozawa, Lifespan of strong solutions to the periodic nonlinear Schr\"odinger equation without gauge invariance,
    J. Evol. Equ., 17 (2017), 1023--1030, doi:10.1007/s00028-016-0364-0, [Mathscinet: MR3707307].
  20. K. Fujiwara and T. Ozawa, Finite time blowup of solutions to the nonlinear Schr\"odinger equation without gauge invariance,
    J. Math. Phys., 57(2016), 082103, doi:10.1063/1.4960725, [bib: MR3535686].
  21. K. Fujiwara and T. Ozawa, Weighted $L^p$-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces,
    J. Math. Soc. Japan, 68(2016), 169--191, doi:10.2969/jmsj/06810169, [Mathscinet: MR3454558].
  22. K. Fujiwara, Remark on local solvability of the Cauchy problem for semirelativistic equations,
    J. Math. Anal. Appl., 432 (2015), 744--748, doi:10.1016/j.jmaa.2015.07.009, [Mathscinet: MR3378389].
  23. K. Fujiwara and T. Ozawa, Remarks on global solutions to the Cauchy problem for semirelativistic equations with power type nonlinearity,
    Int. J. Math. Anal., 9(2015), 2599--2610, doi:10.12988/ijma.2015.58211, [Mathscinet: MR3378389].
  24. K. Fujiwara, S. Machihara, and T. Ozawa, On a system of semirelativistic equations in the energy space,
    Comm. Pure Appl. Anal., 14 (2015), 1343--1355, doi:10.3934/cpaa.2015.14.1343, [Mathscinet: MR3359524].
  25. K. Fujiwara, S. Machihara, and T. Ozawa, Well-posedness for the Cauchy problem for a system of semirelativistic equations,
    Comm. Math. Phys., 338(2015), 367--391, doi:10.1007/s00220-015-2347-3, [Mathscinet: MR3345380].
  26. K. Fujiwara and T. Ozawa, Identities for the difference between the arithmetic and geometric means,
    Int. J. Math. Anal., 8 (2014), 1525--1542, doi:10.12988/ijma.2014.46170, [bib:FuOz14Id].
  27. K. Fujiwara and T. Ozawa, Stability of the Young and Holder inequalities,
    J. Inequal. Appl., 2014:162, doi:10.1186/1029-242X-2014-162, [Mathscinet: MR3346834].
  28. K. Fujiwara and T. Ozawa, Exact remainder formula for the Young inequality and applications,
    Int. J. Math. Anal., 7 (2013), 2723--2735, doi:10.12988/ijma.2013.39230, [Mathscinet: MR3152987].
会議録・論文集 (査読付)
  1. L. Forcella, K. Fujiwara, V. Georgiev, and T. Ozawa, Blow-up or global existence for the fractional Ginzburg-Landau equation in multi-dimensional case,
    New Tools for Nonlinear PDEs and Applications, Birkh\"auser Basel, 179--202 (2019), [Mathscinet:MR4011367].
  2. K. Fujiwara and H. Miyazaki, The derivation of conservation laws for nonlinear Schr\"odinger equations with power type nonlinearities,
    RIMS Kokyuroku Bessatsu, B63, 13--21(2017), [Mathscinet:MR3751978].
  3. K. Fujiwara and T. Ozawa, Remarks on bilinear estimates in the Sobolev spaces,
    RIMS Kokyuroku Bessatsu, B56, 1--9 (2016), [Mathscinet:MR3617712].
  4. K. Fujiwara, S. Machihara, and T. Ozawa, Remark on a semirelativistic equation in the energy space,
    Discrete Contin. Dyn. Syst. 2015, Dynamical systems, differential equations and applications. 10th AIMS Conference. Suppl., 473--478 (2015),
    5. doi:10.3934/proc.2015.0473, [Mathscinet:MR3462480].
論文 (投稿中)
  1. K. Fujiwara and V. Georgiev, On extended lifespan for 1d damped wave equation, arXiv:2212.13845
学位論文