Final value problem governed by a class of time‐space fractional pseudo‐parabolic equations with weak nonlinearities
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DOI: 10.1002/mma.9866
Abstract: We study the final value problem involving a class of semilinear fractional pseudo‐parabolic equations, where the nonlinearity probably takes values in fractional Sobolev spaces. By establishing some estimates for resolvent operators and employing the embedding… read more here.
Keywords: pseudo parabolic; problem; value problem; final value ... See more keywords
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
Some New Families of Exact Solitary Wave Solutions for Pseudo-Parabolic Type Nonlinear Models
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DOI: 10.1155/2024/5762147
Abstract: The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a… read more here.
Keywords: solutions pseudo; new families; pseudo parabolic; wave solutions ... 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
Numerical approximation of the 3rd order pseudo-parabolic equation using collocation technique
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DOI: 10.1186/s13661-024-01956-x
Abstract: This study presents a novel numerical approach for approximating the solution of third-order pseudo-parabolic partial differential equations (PDEs), which exhibit both parabolic and hyperbolic characteristics. The proposed method employs a cubic trigonometric tension B-spline collocation… read more here.
Keywords: order pseudo; order; pseudo parabolic; collocation technique ... See more keywords
Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator
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DOI: 10.1515/math-2025-0144
Abstract: Abstract In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator. The approach is based on the… read more here.
Keywords: baouendi grushin; equation; pseudo parabolic; global existence ... See more keywords