Narrow Results

In this paper, we consider the nonlinear cauchy problem

In this paper, we consider solving a system of fractional differential equations with nonlinear source term. The nonlocal source term is a convolution of an exponential with a kernel. The solved system is able to be seen as a generalization of a number of varied systems of equations with solutions that blows up in a finite time. Under initial conditions, the nontrivial global solutions blow-up and certain assumptions are established by the weak formulation of the problem with some estimation inequalities.

This paper is devoted to the study of the behaviors of the solution to Fujita-type equations on finite graphs. Under certain conditions given by absorption term of the equations, we prove respectively local existence and blow-up results of solutions to Fujita-type equations on finite graphs. Our results contain some previous results as special cases. Finally, we provide some numerical experiments to illustrate the applicability of the obtained results.

In this paper, we study the blow-up problem for Fujita-type equations with a general absorption term $f$ on finite graphs and locally finite graphs, respectively. We prove that if $f$ satisfies appropriate conditions, then the solutions of the equation blow up in finite time. The obtained results are generalization of those given by the author in previous papers. At the end of the paper, we provide some numerical experiments to illustrate the applicability of the obtained results.

In this paper, we deal with the blow-up problems for Fujita-type parabolic system involving time-dependent coefficients on graphs. Under appropriate conditions, we prove that the nonnegative solution of the parabolic system blows up in a finite time on finite graphs and locally finite graphs, respectively. The results obtained extend some previous results of [Y. Lin and Y. Wu, Blow-up problems for nonlinear parabolic equations on locally finite graphs, Acta Math. Sci. Ser. B 38(3) (2018) 843–856; Y. Wu, Local existence and blow-up of solutions to Fujita-type equations involving general absorption term on finite graphs, Fractals 30(2) (2022) 2240053].