Results 11 to 20 of about 243 (185)
Asymptotic behavior for parabolic equations with interior degeneracy
Examples and Counterexamples, 2022 The long time behavior of a class of degenerate parabolic equations in a bounded domain will be considered in the sense that the nonnegative diffusion coefficient a(x)is allowed to vanish in a set of positive measure in the interior of the domain.
María Astudillo +3 more
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Heteroclinic Orbits of Semilinear Parabolic Equations
Journal of Differential Equations, 1996 The authors study attractors of semilinear parabolic problems \[ u_t= u_{xx}+ f(x, u, u_x),\;t> 0,\;0< x< 1,\quad u_x(t, 0)= u_x(t, 1)= 0. \] Here \(f\in C^2\) and appropriate dissipativity conditions are assumed so that the global attractor exists. It is known that the attractor consists of equilibria and heteroclinic orbits connecting them.
Fiedler, Bernold, Rocha, Carlos
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Journal of Function Spaces, 2022 Focusing on the physical context of the thermal explosion model, this paper investigates a semilinear parabolic equation ut=Δu+a∫Ωupdx,x,t∈QT,n·∇u+guu=0,x,t∈ST,ux,0=u0x,x∈Ω with nonlocal sources under nonlinear heat-loss boundary conditions, where a,p>0 ...
Wenyuan Ma, Zhixuan Zhao, Baoqiang Yan
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NUMERICAL QUENCHING FOR A SEMILINEAR PARABOLIC EQUATION
Mathematical Modelling and Analysis, 2008 This paper concerns the study of the numerical approximation for the nonlinear parabolic boundary value problem with the source term leading to the quenching in finite time. We find some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time.
Nabongo, Diabate, Boni, Theodore K.
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Electronic Journal of Qualitative Theory of Differential Equations, 2020 We consider semilinear parabolic equations with nonlinear boundary conditions. We give conditions which guarantee global existence of solutions as well as blow-up in finite time of all solutions with nontrivial initial data.
Alexander Gladkov, Mohammed Guedda
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Convergence of quasilinear parabolic equations to semilinear equations
Discrete and Continuous Dynamical Systems - B, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bezerra, Flank D. M. +2 more
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Modeling Heavy Metal Sorption and Interaction in a Multispecies Biofilm
Mathematics, 2019 A mathematical model able to simulate the physical, chemical and biological interactions prevailing in multispecies biofilms in the presence of a toxic heavy metal is presented.
Berardino D’Acunto +3 more
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A priori estimates and existence of strong solutions for second order semi-linear parabolic systems
Вестник Самарского университета: Естественнонаучная серияThis paper describes an interpolation method for obtaining a priori estimates for strong solutions of semilinear parabolic equations and systems with unbounded singularities in the right-hand side, provided that there is a first a priori estimate in the ...
S. T. Guseynov +2 more
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Blowup of solutions of semilinear parabolic equations
Journal of Mathematical Analysis and Applications, 1988 Consider the blow-up behavior of solutions of a semilinear parabolic equation \[ (1)\quad u_ t+uu_ x-u_{xx}=f(u)\quad (-a0)\), \(u(x,0)=\phi (x ...
Friedman, Avner, Lacey, Andrew A
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The Global Dynamics of Discrete Semilinear Parabolic Equations [PDF]
SIAM Journal on Numerical Analysis, 1993 The authors consider a semilinear parabolic initial value problem possessing absorbing sets. The dynamical properties of various fininte difference and finite element schemes are analysed. The existence of absorbing sets, Lyapunov functions and attractors for the approximation are studied. The authors construct implicit schemes for which absorbing sets
Elliott, C. M., Stuart, A. M.
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