Blow-Up Phenomena for a Class of Parabolic or Pseudo-parabolic Equation with Nonlocal Source
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DOI: 10.1007/s00009-021-01735-3
Abstract: In this paper, we consider a class of parabolic or pseudo-parabolic equation with nonlocal source term: $$\begin{aligned} u_t-\nu \triangle u_t-\hbox {div}(\rho (|\nabla u|)^2\nabla u)=u^p(x,t)\int _{\Omega }k(x,y)u^{p+1}(y,t)dy, \end{aligned}$$ where $$\nu \ge 0$$ and $$p>0$$ . Using… read more here.
Keywords: pseudo parabolic; equation nonlocal; class parabolic; parabolic equation ... See more keywords
Global Existence and Blow-up in Finite Time for a Class of Finitely Degenerate Semilinear Pseudo-parabolic Equations
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DOI: 10.1007/s10114-019-8037-x
Abstract: In this paper, we study the initial-boundary value problem for the semilinear pseudo-parabolic equations ut − ΔXut − ΔXu = |u|p−1u, where X = (X1,X2,…,Xm) is a system of real smooth vector fields which satisfy… read more here.
Keywords: time; finitely degenerate; pseudo parabolic; parabolic equations ... See more keywords
On the well-posedness of a nonlinear pseudo-parabolic equation
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DOI: 10.1007/s11784-020-00813-5
Abstract: In this paper we consider the Cauchy problem for the pseudo-parabolic equation: $$\begin{aligned} \dfrac{\partial }{\partial t} \left( u + \mu (-\Delta )^{s_1} u\right) + (-\Delta )^{s_2} u = f(u),\quad x \in \Omega ,~ t>0. \end{aligned}$$… read more here.
Keywords: well posedness; pseudo parabolic; posedness nonlinear; parabolic equation ... See more keywords
Time-discretization schema for a semilinear pseudo-parabolic equation with integral conditions
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DOI: 10.1016/j.apnum.2019.09.002
Abstract: Abstract In this paper, we use the Rothe time-discretization method to prove the existence and uniqueness of a strong solution of a semilinear pseudo-parabolic equation with integral conditions. We also provided an example to illustrate… read more here.
Keywords: pseudo parabolic; parabolic equation; time discretization; semilinear pseudo ... See more keywords
Stability of a class of problems for time-space fractional pseudo-parabolic equation with datum measured at terminal time
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DOI: 10.1016/j.apnum.2021.05.009
Abstract: Abstract We consider terminal value problems for time-space fractional pseudo-parabolic equation subjected to a final/terminal value condition. In fact, fractional orders α , s are not exactly known in modeling. These are determined experimentally. The… read more here.
Keywords: problems time; time; pseudo parabolic; fractional pseudo ... See more keywords
Global existence and blow-up for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity-II
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DOI: 10.1080/00036811.2019.1695784
Abstract: ABSTRACT This paper deals with the following mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity in a bounded domain with zero Dirichlet boundary condition, which was studied in our previous paper [J Math Anal Appl.… read more here.
Keywords: global existence; pseudo parabolic; mixed pseudo; existence blow ... See more keywords
Blow-up phenomena and lifespan for a quasi-linear pseudo-parabolic equation at arbitrary initial energy level
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DOI: 10.1186/s13661-018-1079-7
Abstract: AbstractIn this paper, we continue to study the initial boundary value problem of the quasi-linear pseudo-parabolic equation ut−△ut−△u−div(|∇u|2q∇u)=up$$ u_{t}-\triangle u_{t}-\triangle u-\operatorname{div}\bigl(| \nabla u|^{2q}\nabla u\bigr)=u^{p} $$ which was studied by Peng et al. (Appl. Math. Lett.… read more here.
Keywords: parabolic equation; pseudo parabolic; energy; linear pseudo ... See more keywords
An inverse problem for the pseudo-parabolic equation with p-Laplacian
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DOI: 10.3934/eect.2021005
Abstract: In this article, we study the inverse problem of determining the right side of the pseudo-parabolic equation with a p-Laplacian and nonlocal integral overdetermination condition. The existence of solutions in a local and global time… read more here.
Keywords: equation laplacian; problem; pseudo parabolic; parabolic equation ... See more keywords