In this paper we consider the nonlinearly damped semilinear wave equation utt âˆ’âˆ†u + aut |ut|mâˆ’2 = bu|u|pâˆ’2 associated with initial and Dirichlet boundary conditions. We prove that any strongâ€¦ (More)

In this paper we consider the Cauchy problem for the nonlinearly damped wave equation with nonlinear source utt âˆ’âˆ†u + aut|ut|mâˆ’2 = bu|u|pâˆ’2, p > m. We prove that given any time T > 0, there existâ€¦ (More)

In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one-dimensional bounded domain. The system has two dissipative mechanisms being present in the equation forâ€¦ (More)

Available online xxxx Keywords: Nonlinear heat equation Blow up Sobolev spaces with variable exponents a b s t r a c t In this paper we consider a nonlinear heat equation with nonlinearities ofâ€¦ (More)

In this work we consider an initial one-point boundary value problem to the heat equation with the Bessel operator ut âˆ’ (uxx + 1 xux) = |u| pâˆ’2u. We first prove a local existence result. Then we showâ€¦ (More)