Results 1 to 10 of about 221 (166)
Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations
Mathematics, 2023 We formulate a quasilinear parabolic equation describing the behavior of the global-in-time solution to a semilinear parabolic equation. We study this equation in accordance with the blow-up and quenching patterns of the solution to the original ...
Katsuyuki Ishii +2 more
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Lack of smoothing for bounded solutions of a semilinear parabolic equation
Advances in Nonlinear Analysis, 2020 We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all t > 0.
Fila Marek, Lankeit Johannes
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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.
Diabate Nabongo, Theodore K. Boni
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A triviality result for semilinear parabolic equations
Mathematics in Engineering, 2022 We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation \begin{equation*} u_{t}=Δu + |u|^{p} \end{equation*} on complete Riemannian manifolds of dimension $n \geq 5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $\frac{n+2}{n-2}$.
Giovanni Catino +2 more
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Blow-Up of the Solution for a Semilinear Parabolic Problem with a Mixed Source
Mathematics, 2022 A semilinear parabolic equation with the Dirichlet boundary condition is examined. The reaction source is a mixed nonlinear function. This paper investigates the existence and uniqueness of a solution.
Wai Yuen Chan
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Null controllability of a semilinear degenerate parabolic equation with a gradient term
Boundary Value Problems, 2020 This paper concerns the null controllability of a semilinear control system governed by degenerate parabolic equation with a gradient term, where the nonlinearity of the problem is involved with the first derivative. We first establish the well-posedness
Fengdan Xu, Qian Zhou, Yuanyuan Nie
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Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion
Demonstratio Mathematica, 2020 In this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is
Villa-Morales José
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Blow-up time of solutions to a class of pseudo-parabolic equations
Comptes Rendus. Mécanique, 2023 In this paper, we study the Dirichlet problem for a semilinear pseudo-parabolic equation. By using the energy estimates and ordinary differential inequalities, we studied the upper and lower bounds of blow-up time of the solutions.
Zhou, Jun, Wang, Xiongrui
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On a semilinear parabolic equation [PDF]
Proceedings of the American Mathematical Society, 2006 We introduce a general class of potentials V = V ( x ,
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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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