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math.AP2024
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…
math.AP2024
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…
math.AP2024
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…