Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case

By Wenhui Chen, A. Palmieri. Discrete and Continuous Dynamical Systems. Series A, 2019

64 citations recorded by the source corpus.

In this work, the Cauchy problem for the semilinear Moore-Gibson-Thompson (MGT) equation with power nonlinearity $|u|^p$ on the right-hand side is studied. Applying $L^2-L^2$ estimates and a fixed point theorem, we obtain local (in time) existence of solutions to the semilinear MGT equation. Then, the blow-up of local in time solutions is proved by using an iteration method, under certain sign assumption for initial data, and providing that the exponent of the power of the nonlinearity fulfills $1 1$ for $n=1$. Here the Strauss exponent $p_{\mathrm{Str}}(n)$ is the critical exponent for the semilinear wave equation with power nonlinearity.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f46f6ce56ca8965b8d450e0c0fd1d6901fabf3f1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Wenhui Chen
2. Ryo Ikehata
3. M. DʼAbbicco

In Mathematical Physics

1. Wenhui Chen
2. Ryo Ikehata
3. M. DʼAbbicco
4. Hiroshi Takeda
5. Kenji Nishihara
6. M. Ebert

In Statistical and Nonlinear Physics

1. Ryo Ikehata
2. Wenhui Chen

Citations in the corpus

• The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case (2020, methodology): “Concerning other studies for the linear or nonlinear MGT equations, we refer interested readers to the related works [40, 50, 19, 34, 33, 39, 32, 38, 47, 7, 15, 37, 16, 36, 46, 5, 1, 14, 6, 48, 45, 10, 11, 4, 41, 42] and references therein.”