Ireneo Peral

On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term

AbstractWe study questions of existence, uniqueness and asymptotic behaviour for the solutions of u(x, t) of the problem

Semilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions

\begin{gathered} {\text{ }}u_t - \Delta u = \lambda e^u ,{\text{ }}\lambda {\text{ > 0, }}t > 0,{\text{ }}x{\text{ }}\varepsilon B, \hfill \\ (P){\text{ }}u(x,0) = u_0 (x),{\text{ }}x{\text{ }}\varepsilon B, \hfill \\ {\text{ }}u(x,t) = 0{\text{ }}on{\text{ }}\partial B \times (0,\infty ), \hfill \\ \end{gathered}

A Widder’s Type Theorem for the Heat Equation with Nonlocal Diffusion

where B is the unit ball

Semilinear problems for the fractional laplacian with a singular nonlinearity

\{ x\varepsilon R^N :|x|{\text{ }} \leqq {\text{ }}1\} {\text{ and }}N \geqq 3

Results on Parabolic Equations Related to Some Caffarelli--Kohn--Nirenberg Inequalities

. Our interest is focused on the parameter λ0=2(N−2) for which (P) admits a singular stationary solution of the form