Blow-up of the solution of a nonlinear system of equations with positive energy

Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level

“…We also obtained the finite time blow-up result for certain solutions whose initial data have arbitrary high initial energy, see [20][21][22][23]. For details of the study of other kinds of evolution equations, we refer the reader to [24][25][26][27][28][29][30][31][32][33][34][35].…”

Well-posedness issues for some critical coupled non-linear Klein-Gordon equations

“…The existence of global/nonglobal solutions for a non-linear coupled wave system was discussed by many authors [30,31,32]. Recently, a coupled non-linear Klein-Gordon equation with damping term was treated by Pişkin and Korpusov [12,23,24].…”

Blow-Up of Solutions to Semilinear Nonautonomous Wave Equations with Robin Boundary Conditions

“…There have been many works devoted to the problems of global non-existence and blow up of solutions to initial boundary value problems for nonlinear wave equations (see, e.g., [1], [8], [2], [3], [11], [10] and references therein). In majority of these papers sufficient conditions of blow up of solutions in a finite time of initial boundary value problems for various nonlinear wave equations under the homogeneous Dirichlet or Neumann boundary conditions, nonlinear boundary conditions and dynamic boundary conditions are provided.…”