Cauchy problems of semilinear pseudo-parabolic equations ✩

By Yang Cao, Jingxue Yin, Chunpeng Wang. 2009

156 citations recorded by the source corpus.

Abstract This paper concerns with the Cauchy problems of semilinear pseudo-parabolic equations. After establishing the necessary existence, uniqueness and comparison principle for mild solutions, which are also classical ones provided that the initial data are appropriately smooth, we investigate large time behavior of solutions. It is shown that there still exist the critical global existence exponent and the critical Fujita exponent for pseudo-parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/80669cb46726e4793761588e8e71195c3d6403b9

Citations in the corpus

• Semilinear Caputo time-fractional pseudo-parabolic equations (2021, unknown): “As shown in [11], a function u is a mild solution of (P1) if u ∈ C([0, T ];L(2)(Ω)) and satisfies the following integral equation (set L = −∆) u(t) =Eα,1 ( −L(I +mL)−1tα ) u0 + (I +mL)−1 ∫ t”