Qualitative properties for solutions of semilinear heat equations with strong absorption

Holomorphic Solutions of Semilinear Heat Equations

with φ ∈ L(R), where P is a polynomial vanishing at the origin and ∆ stands for the Laplacian with respect to x. The analyticity in time of the solutions of a semilinear heat equation has been considered by many authors. For example Ōuchi [2] treated the analyticity in time of the solutions of certain initial boundary value problems with bounded continuous initial functions, which include (1) i...

Global Solutions of Semilinear Heat Equations in Hilbert Spaces

The existence, uniqueness, regularity and asymptotic behavior of global solutions of semilinear heat equations in Hilbert spaces are studied by developing new results in the theory of one-parameter strongly continuous semigroups of bounded linear operators. Applications to special semilinear heat equations in L(R) governed by pseudo-differential operators are given.

Boundedness of solutions for semilinear duffing equations

Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on R

We consider bounded solutions of the semilinear heat equation ut = uxx+f(u) on R, where f is of a bistable type. We show that there always exist bounded solutions whose ω-limit set with respect to the locally uniform convergence contains functions which are not steady states. For balanced bistable nonlinearities, there are examples of such solutions with initial values u(x, 0) converging to 0 a...

Strong Solutions for Semilinear Wave Equations with Damping and Source Terms

This paper deals with local existence of strong solutions for semilinear wave equations with power-like interior damping and source terms. A long standing restriction on the range of exponents for the two nonlinearities governs the literature on wellposedness of weak solutions of finite energy. We show that this restriction may be eliminated for the existence of higher regularity solutions by e...