In this work, the local and global existence of weak solutions by using Faedo-Galerkin method, finite time blow up solution with positive initial energy general decay are discussed. Finally, we consider exponential growth sufficient conditions. This work generalizes improves earlier results in literature, see [L.X. Truong N. Van Y, On a class nonlinear heat equations viscoelastic term, Comput. ...

in exploration seismology, migration refers to a multi-channel processing step that attempts to spatially re-position events and improve focusing. before migration, seismic data is usually displayed with traces plotted at the surface location of the receivers and with a vertical time axis. this means that dipping reflections are systematically mispositioned in the lateral coordinate and the ver...

The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the ti...

The present paper deals with a parametrized Kirchhoff type problem involving critical nonlinearity in high dimension. Existence, non existence and multiplicity of solutions are obtained under the effect subcritical perturbation by combining variational properties careful analysis fiber maps energy functional associated to problem. particular case pure power is also addressed. Through study Neha...

We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for $(\text{PS})$ condition to hold. Then prove some existence and multiplicity results using tools from Morse theory, in particular, notion cohomological local splitting eigenvalues based on Fadell-Rabinowitz index.