3 citations · 7 across the 12 of their papers we have counts for
14 papers
Nondegeneracy and asymptotic behavior of type I blow-up for semilinear heat equations with general nonlinearities
Yohei Fujishima, Ryoto Ichiya, Norisuke Ioku
We study the local asymptotic behavior of nonnegative type I blow-up solutions to semilinear heat equations with nonlinearities that need not be scale invariant. Using a quasi-simi…
Multiplicity of singular solutions for semilinear elliptic equations with superlinear source terms
Yohei Fujishima, Norisuke Ioku
This paper investigates the multiplicity of singular solutions for the nonlinear elliptic equation near the origin. Applying the classification of nonlinear functions a…
Non-uniqueness of mild solutions for 2d-heat equations with singular initial data
Yohei Fujishima, Norisuke Ioku, Bernhard Ruf +1
In a recent article by the authors [15] it was shown that wide classes of semilinear elliptic equations with exponential type nonlinearities admit singular radial solutions on…
Atmospheric Predictability Beyond 30 Days with Machine Learning
P. Trent Vonich, Gregory J. Hakim
Atmospheric predictability research has long held that rapid error growth at small spatial scales imposes an intrinsic limit of roughly two weeks on deterministic weather forecast…
Uniform boundedness and blow-up rate of solutions in non-scale-invariant superlinear heat equations
Yohei Fujishima, Toru Kan
For superlinear heat equations with the Dirichlet boundary condition, the estimates of radially symmetric solutions are studied. In particular, the uniform boundedness o…
Existence of solutions for a semilinear parabolic system with singular initial data
Yohei Fujishima, Kazuhiro Ishige, Tatsuki Kawakami
Let be a solution to the Cauchy problem for a semilinear parabolic system \[ \mathrm{(P)} \qquad \cases{ \partial_t u=D_1Δu+v^p\quad & $\quad\mbox{in}\quad{\mathbb{R}}^N\ti…
Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions
Yohei Fujishima, Norisuke Ioku, Bernhard Ruf +1
By introducing a new classification of the growth rate of exponential functions, singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearitie…
Local solvability and dilation-critical singularities of supercritical fractional heat equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for loca…
Quasi self-similarity and its application to the global in time solvability of a superlinear heat equation
Yohei Fujishima, Norisuke Ioku
This paper concerns the global in time existence of solutions for a semilinear heat equation \begin{equation} \tag{P} \label{eq:P} \begin{cases} \partial_t u = Δu + f(u), &x\in \ma…
Solvability of Superlinear Fractional Parabolic Equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our condi…
Optimal singularities of initial functions for solvability of a semilinear parabolic system
Yohei Fujishima, Kazuhiro Ishige
Let be a nonnegative solution to the semilinear parabolic system \[ \mbox{(P)} \qquad \cases{ \partial_t u=D_1Δu+v^p, & \\ \partial_t v=D_2Δv+u^q,…
Initial traces and solvability of Cauchy problem to a semilinear parabolic system
Yohei Fujishima, Kazuhiro Ishige
Let be a solution to a semilinear parabolic system \[ \mbox{(P)} \qquad \begin{cases} \partial_t u=D_1Δu+v^p\quad & \quad\mbox{in}\quad{\bf R}^N\times(0,T),\\ \partial_t v=…
Critical exponent for the global existence of solutions to a nonlinear degenerate/singular parabolic equation
Yohei Fujishima, Tatsuki Kawakami, Yannick Sire
We investigate a non-homogeneous nonlinear heat equation which involves degenerate or singular coefficients belonging to the class of functions. We prove the existence of a F…
Existence and nonexistence of solutions for the heat equation with a superlinear source term
Yohei Fujishima, Norisuke Ioku
Classification theory on the existence and non-existence of local in time solutions for initial value problems of nonlinear heat equations are investigated. Without assuming a conc…