Classical Solutions of Parabolic Initial-Boundary-Value Problems and HӧRmander Spaces

2017 ◽  
Vol 68 (9) ◽  
pp. 1412-1423
Author(s):  
V. M. Los’
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Classical Solutions ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

scholarly journals Initial Boundary Value Problems of Semi-Linear Sub-Diffusion with Gradient Terms

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1665
Author(s):  
Yabing Gao ◽  
Yongxiang Li
Keyword(s):  
Boundary Value Problems ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Fractional Power ◽  
Initial Boundary ◽  
Classical Solutions ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

We consider the existence and uniqueness of the saturated classical solutions and the positive classical solutions to initial boundary value problems of semi-linear sub-diffusion with gradient terms. Applying this to the fractional power of the sectorial operator theory and the imbedding theory in the interpolation spaces, where the nonlinear term satisfies more general conditions, we obtain the existence and uniqueness of the saturated classical solutions. The results obtained generalize the recent conclusions on this topic. Finally, an example is given to illustrate the feasibility of our main results.

Hölder continuous dependence in nonlinear elastodynamics

1986 ◽  
Vol 102 (1-2) ◽  
pp. 49-60 ◽  
Author(s):  
Stan Chiriţă
Keyword(s):  
Boundary Value Problems ◽  
Continuous Dependence ◽  
Boundary Value ◽  
Initial Boundary ◽  
Classical Solutions ◽  
Initial Boundary Value Problems ◽  
Hölder Continuous ◽  
Nonlinear Elastodynamics ◽  
Body Forces ◽  
Initial Boundary Value

SynopsisIn this paper we establish conditions to prove that if classical solutions to the initial boundary value problems for nonlinear elastodynamics exist, then they depend Hölder continuously on their initialdata and body forces.

Sign in / Sign up

Export Citation Format

Share Document