scholarly journals Differentiability of weak solutions to an abstract inhomogeneous differential equation

1981 ◽  
Vol 82 (3) ◽  
pp. 425-425 ◽  
Author(s):  
C. C. Travis
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Inhomogeneous Differential Equation

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

scholarly journals Asymptotic Behavior of Weak Solutions to the Generalized Nonlinear Partial Differential Equation Model

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Min Wu ◽  
Yousheng Wu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Asymptotic Behavior ◽  
Weak Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Equation Model ◽  
Differential Equation Model ◽  
Partial Differential ◽  
Large Perturbation ◽  
Partial Differential Equation Model

This paper investigates the asymptotic behavior of weak solutions to the generalized nonlinear partial differential equation model. It is proved that every perturbed weak solution of the perturbed generalized nonlinear partial differential equations asymptotically converges to the solution of the original system under the large perturbation.

scholarly journals Hölder continuity of solutions of some degenerate elliptic differential equations

2000 ◽  
Vol 62 (3) ◽  
pp. 369-377 ◽  
Author(s):  
Ahmed Mohammed
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Weak Solutions ◽  
Function Spaces ◽  
Elliptic Differential Equation ◽  
Holder Continuity ◽  
Hölder Continuous ◽  
Elliptic Differential Equations ◽  
Continuity Of Solutions ◽  
Degenerate Elliptic

Weak solutions of the degenerate elliptic differential equation Lu := −div(A (x)∇u)+b·∇u+Vu = f, with |b|2ω−1, V, f in some appropriate function spaces, will be shown to be Hölder continuous.

19.—Concavity and the Evolutionary Properties of a Class of General Materials

1975 ◽  
Vol 72 (3) ◽  
pp. 239-243 ◽  
Author(s):  
R. N. Hills ◽  
R. J. Knops
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Initial Data ◽  
Linear Differential Equation ◽  
Weak Solutions ◽  
Finite Time ◽  
Escape Time ◽  
Non Linear ◽  
Linear Differential

Concavity arguments have been used by Knops, Levine and Payne [1] to discuss evolutionary properties of weak solutions to an abstract non-linear differential equation in a Hilbert space. These authors demonstrate that provided the non-linearity is suitably restricted and for specified initial data, the norm of the solution becomes unbounded in a finite time. In other words, the solution possesses a finite escape time.

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