Blow-up And Decay For A Class Of Strongly Damped Nonlinear Wave Equations

In recent years,with the rapid development of cross-application subjects such as biomathematics and mathematical physics and the wide application of nonlinear wave equation in economic engineering and other fields,the nonlinear wave equation has at-tracted more and more attention from scholars at home and abroad.In particular,the global existence of the solution of the nonlinear wave equation and the explosion phe-nomenon become the research hotpot.Section 1 is the introduction,which mainly introduces the research background and development status of the initial boundary value problems for a class of p-Laplacian nonlinear wave equations with logarithmic nonlinear term.Section 2 mainly introduces the basic definition of weak solution and the abbreviation symbol,and gives the important lemma which will be used to prove the main results.Section 3 introduces the important logarithmic Sobolev inequality and state the main results.In Section 4,the global existence of the weak solution,the decay of energy,the blow-up of the solution in finite time and the upper and lower bounds of the blow-up time are proved in detail.