论文标题
对具有梯度项的非线性抛物线方程的半差异溶液的爆炸
Blow-up of semi-discrete solution of a nonlinear parabolic equation with gradient term
论文作者
论文摘要
本文涉及非线性抛物线问题中爆破现象的近似。我们考虑方程u_t = u_xx +| u |^p -b（x）| u_x |^q在一个有界域中，我们研究了半分化问题的行为。在某些假设下，我们显示了半分化解决方案的存在和统一性，我们表明它在有限的时间内炸毁了，我们证明了半分化问题的收敛性。最后，我们给出了爆炸速率和半分化溶液的爆炸时间
This paper is concerned with approximation of blow-up phenomena in nonlinear parabolic problems. We consider the equation u_t = u_xx +|u|^p -b(x)|u_x|^q in a bounded domain, we study the behavior of the semidiscrete problem. Under some assumptions we show existence and unicity of the semidiscrete solution, we show that it blows up in a finite time and we prove the convergence of the semidiscrete problem. Finally, we give an approximation of the blow up rate and the blow up time of the semidiscrete solution
