5 papers · 1 filter
Well-posedness of Heat Equations with Nonlinearities of Arbitrarily Rapid Growth
Yohei Fujishima, Kotaro Hisa, Robert Laister
We address local- and global-in-time well-posedness of the Cauchy problem for nonlinear heat equations without imposing growth rate restrictions on the nonlinearity a priori. Our r…
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…
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…
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_1Îu+v^p\quad & $\quad\mbox{in}\quad{\mathbb{R}}^N\t…