Semilinear parabolic equation
General decay rate estimates for a semilinear parabolic equation with memory term and mixed boundary condition
... ear parabolic equations and systems with or without memory ...the semilinear parabolic equation; see the monographs [, ] and the survey papers ...
11
Sharp threshold for blow-up and global existence in a semilinear parabolic equation with variable source
... This paper deals with a semilinear parabolic equation with variable source under the case that the initial energy is less than the potential well depth. We deduce a sharp threshold for blow-up and ...
12
Solving the inverse problem of determining an unknown control parameter in a semilinear parabolic equation
... In this paper, the inverse problem of determining an unknown control parameter in a semilinear parabolic equation under an integral overde- termination condition is considered. By using the WHAM, an ...
11
Blow up theorems of Fujita type for a semilinear parabolic equation with a gradient term
... This paper deals with the existence and non-existence of the global solutions to the Cauchy problem of a semilinear parabolic equation with a gradient term. The blow-up theorems of Fujita type are ...
12
Asymptotic speed of propagation for a viscous semilinear parabolic equation
... This equation can be interpreted as a simplified model for the motion of an interface in a material under the combined effect of a spatially heterogeneous medium, given by g, and the surface ...
9
Global existence and asymptotic behavior of solutions to a semilinear parabolic equation on Carnot groups
... where | · | denotes the Euclidean distance on R . In particular d satisfies the triangle in- equality via (.). For r > , we can also define the ball with center (ξ , t) and radius r with respect to the ...
18
On basin of zero solutions to a semilinear parabolic equation with Ornstein Uhlenbeck operator
... linear parabolic equations, the Ornstein-Uhlenbeck operator contributes good properties to their solutions such as ergodicity and ...linear parabolic equations, a contribution of the Ornstein-Uhlenbeck ...
10
Singularity analysis for a semilinear integro differential equation with nonlinear memory boundary
... a semilinear parabolic equation with nonlinear memory both in the reaction term and the boundary ...of semilinear parabolic equations with various nonlocal reaction ...
17
A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations
... a semilinear parabolic equation with con- tinuous, increasing nonlinearity f ...evolution equation; (c) monotonicity of the semigroup S β ...
12
Critical global asymptotics in higher order semilinear parabolic equations
... 2mth-order semilinear parabolic equation in the critical case, where a special nonlinear interaction between operators produces asymptotics per- turbed by logarithmic ...1) semilinear and ...
17
A Consecutive Quasilinearization Method for the Optimal Boundary Control of Semilinear Parabolic Equations
... A consecutive quasilinearization method was proposed for the optimal boundary control problems with quadrat- ic objective of tracking type and a semilinear parabolic equation with mixed boundary as ...
16
Boundary gradient exact enlarged controllability of semilinear parabolic problems
... Motivated by the arguments above, in this paper, our goal is to study the regional boundary enlarged controllability of the gradient. For that we consider a semilinear system of parabolic equations where ...
6
Adaptive fully-discrete finite element methods for nonlinear quadratic parabolic boundary optimal control
... parabolic equation. To our best knowledge, in the context of nonlinear parabolic boundary optimal control problems, these estimates are ...quadratic parabolic boundary optimal control ...
18
An approximation scheme for semilinear parabolic PDEs with convex and coercive Hamiltonians
... underlying equation with respect to its ...original equation), the shaking coefficients technique only gives either an upper or a lower bound for the approximation error, but not ...
29
Asymptotic behavior of solutions to a class of semilinear parabolic equations
... quasilinear parabolic equations and sys- tems in various of geometries (whole spaces, cones, and exterior domains) with nonlinear reactions or nonhomogeneous boundary conditions, and even degenerate equations in ...
9
Remarks on the approximate and null controllability of semilinear parabolic equations
... Finally, observe that the arguments used in the proof of theorem 2.1 (and corollary 3.1) also serve, with appropriate changes, to investigate the controlla- bility properties of some quasilinear parabolic systems. ...
9
Singularities of the minimum time function for semilinear parabolic systems
... However, the open question remains whether the minimum time function associated with a system of the form (1) may still be nonsmooth. In section 2 of this paper we provide such an example for a 2 × 2 reaction diffusion ...
14
Regional Observability with Constraints on the State of Semilinear Parabolic Systems
... In this paper, we study for the first time the concept of regional observability with constraints on the state for a class of semilinear parabolic systems (also called enlarged observability). The ...
15
Blowup Analysis for a Semilinear Parabolic System with Nonlocal Boundary Condition
... This paper deals with the properties of positive solutions to a semilinear parabolic system with nonlocal boundary condition. We first give the criteria for finite time blowup or global existence, which ...
14
Stability and numerical approximation for a spacial class of semilinear parabolic equations on the Lipschitz bounded regions: Sivashinsky equation
... Investigated by authors of [6], a set of background cells were required to evaluate the integrals resulted from the use of the Galerkin weak-form. Global numerical integrations were needed to obtain the coefficient ...
12