Results 41 to 50 of about 396,174 (280)

Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms

Abstract and Applied Analysis, 2018
We study systems with different diffusions (local and nonlocal), mixed boundary conditions, and reaction terms. We prove existence and uniqueness of the solutions and then analyze global existence vs blow up in finite time.
Mauricio Bogoya, Julio D. Rossi
doaj   +1 more source

Blow-up Rate Estimates for Parabolic Equations

, 2012
We consider the blow-up sets and the upper blow-up rate estimates for two parabolic problems defined in a ball.
Rasheed, Maan A., Chlebik, Miroslav
openaire   +2 more sources

Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions

Journal of Applied Mathematics, 2008
We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut=uxx−a(x,t)f(u ...
Louis A. Assalé, Théodore K. Boni, Diabate Nabongo   +2 more
doaj   +1 more source

On decay and blow-up of solutions for a system of viscoelastic equations with weak damping and source terms

Journal of Inequalities and Applications, 2019
In this article, we investigate a system of two viscoelastic equations with Dirichlet boundary conditions. Under some suitable assumptions on the function gi(⋅) $g_{i}(\cdot )$, fi(⋅,⋅) $f_{i}(\cdot ,\cdot )$ ( i=1,2 $i=1,2$) and the initial data, we ...
Luofei He
doaj   +1 more source

Blow-Up Rate Estimates for Semilinear Parabolic Systems

Journal of Differential Equations, 2001
Let \(\Omega\) be a smoothly bounded domain in \(\mathbb R^n\), \(p,q>0\), \(pq>1\), \(\alpha:=(p+1)/(pq-1)\), \(\beta:=(q+1)/(pq-1)\). Consider the parabolic system \(u_t=\Delta u+v^p\), \(v_t=\Delta v+u^q\), \(x\in\Omega\), \(t>0\), complemented by the homogeneous Dirichlet boundary conditions and the initial conditions \(u(x,0)=u_0(x)\), \(v(x,0 ...
openaire   +1 more source

Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary Condition

Abstract and Applied Analysis, 2014
We discuss the global and blow-up solutions of the following nonlinear parabolic problems with a gradient term under Robin boundary conditions: (b(u))t=∇·(h(t)k(x)a(u)∇u)+f(x,u,|∇u|2,t), in D×(0,T), (∂u/∂n)+γu=0, on ∂D×(0,T), u(x,0)=u0(x)>0, in D¯, where
Lingling Zhang, Hui Wang
doaj   +1 more source

Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition

Electronic Journal of Qualitative Theory of Differential Equations, 2010
In this paper, we consider a semilinear parabolic equation $$u_t=\Delta u+u^q\int_0^tu^p(x,s)ds,\quad x\in \Omega,\quad t>0$$ with nonlocal nonlinear boundary condition $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omega\varphi(x,y) u^l(y,t)dy$ and ...
Dengming Liu, Chunlai Mu
doaj   +1 more source

The boundary blow-up rate of large solutions

Journal of Differential Equations, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Manufacturing Continuous Fiber‐Reinforced Printing Filaments: Development of a Post‐Consolidation Unit

Advanced Engineering Materials, EarlyView.
A novel, temperature‐controlled post‐consolidation unit is developed to test its potential to improve the melt impregnation process used to manufacture continuous fiber‐reinforced filaments for additive manufacturing of high‐performance thermoplastics.
Daniel Beermann, Patrick Schiebel, David May   +2 more
wiley   +1 more source

Finite-time singularities in the dynamical evolution of contact lines [PDF]

, 2013
We study finite-time singularities in the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a ...
Giniyatullin, A. R., Pelinovsky, D. E.
core