Class Of Pseudo-parabolic Equations Research Articles

Blow-up in finite time for a pseudo-parabolic equation with variable exponents

This paper investigates the blow-up phenomenon in a class of pseudo-parabolic equations with variable exponents. We demonstrate that the solutions to the corresponding initial boundary value problem blow up in finite time when the initial energy is positive and the initial data is sufficiently large. Recently, a blow-up result for this equation with non-positive initial energy was established in Applied Mathematics Letters (2023). Notably, we have eliminated the conditions typically imposed by Sobolev's inequality, this process is applicable to a variety of equations.

On a nonlocal problem for a Caputo time‐fractional pseudoparabolic equation

In this paper, we consider a class of pseudoparabolic equations with the nonlocal condition and the Caputo derivative. Two cases of problems (1–2) will be studied, which are linear case and nonlinear case. For the first case, we establish the existence, the uniqueness, and some regularity results by using some estimates technique and Sobolev embeddings. Second, the Banach fixed‐point theorem will be applied to the nonlinear case to prove the existence and the uniqueness of the mild solution.

Blow-up and exponential decay of solutions to a class of pseudo-parabolic equation

Blow-up and exponential decay of solutions to a class of pseudo-parabolic equation