Weak Convergence: The Perturbed Test Function Method

AbstractIn this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solutions.

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Nonexistence of solutions for parabolic inequalities in unbounded cone-like domains via the test function method

Journal of Evolution Equations ◽

10.1007/pl00012600 ◽

2002 ◽

Vol 2 (4) ◽

pp. 459-470 ◽

Cited By ~ 5

Author(s):

Gennady G. Laptev

Keyword(s):

Function Method ◽

Test Function ◽

Nonexistence Of Solutions ◽

Test Function Method ◽

Parabolic Inequalities

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Nonexistence Results for Some Classes of Nonlinear Fractional Differential Inequalities

Journal of Function Spaces ◽

10.1155/2020/8814785 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Mohamed Jleli ◽

Bessem Samet

Keyword(s):

Function Method ◽

Sufficient Conditions ◽

Global Solutions ◽

Differential Inequalities ◽

Test Function ◽

Fractional Differential ◽

Test Function Method

We study the nonexistence of global solutions for new classes of nonlinear fractional differential inequalities. Namely, sufficient conditions are provided so that the considered problems admit no global solutions. The proofs of our results are based on the test function method and some integral estimates.

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Nonexistence of solutions for quasilinear hyperbolic inequalities

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02685-w ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Suping Xiao ◽

Zhong Bo Fang

Keyword(s):

Weak Solutions ◽

Function Method ◽

Source Term ◽

Cauchy Problems ◽

Global Weak Solutions ◽

Test Function ◽

Singular Source ◽

Nonexistence Of Solutions ◽

Test Function Method

AbstractIn this paper, we study the Cauchy problems for quasilinear hyperbolic inequalities with nonlocal singular source term and prove the nonexistence of global weak solutions in the homogeneous and nonhomogeneous cases by the test function method.

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Solving Jimbo-Miwa equation by using the new test function method

2011 Seventh International Conference on Natural Computation ◽

10.1109/icnc.2011.6022548 ◽

2011 ◽

Author(s):

Yeqiong Shi ◽

Song Han

Keyword(s):

Function Method ◽

Test Function ◽

Test Function Method

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Blow-Up of Solutions to Fractional-in-Space Burgers-Type Equations

Fractal and Fractional ◽

10.3390/fractalfract5040249 ◽

2021 ◽

Vol 5 (4) ◽

pp. 249

Author(s):

Munirah Alotaibi ◽

Mohamed Jleli ◽

Bessem Samet

Keyword(s):

Finite Time ◽

Function Method ◽

Burgers Equation ◽

Blow Up ◽

Sufficient Conditions ◽

Bounded Domains ◽

Initial Value ◽

Test Function ◽

Burgers Type Equations ◽

Test Function Method

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditions depend on the initial value and the boundary conditions. Some examples are provided to illustrate our obtained results. In the proofs of our main results, we make use of the test function method and some integral inequalities.

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Nonexistence of Global Solutions to Higher-Order Time-Fractional Evolution Inequalities with Subcritical Degeneracy

Mathematics ◽

10.3390/math9212765 ◽

2021 ◽

Vol 9 (21) ◽

pp. 2765

Author(s):

Ravi P. Agarwal ◽

Soha Mohammad Alhumayan ◽

Mohamed Jleli ◽

Bessem Samet

Keyword(s):

Weak Solutions ◽

Function Method ◽

Sufficient Conditions ◽

Global Solutions ◽

Higher Order ◽

Global Weak Solutions ◽

Test Function ◽

Test Function Method

In this paper, we study the nonexistence of global weak solutions to higher-order time-fractional evolution inequalities with subcritical degeneracy. Using the test function method and some integral estimates, we establish sufficient conditions depending on the parameters of the problems so that global weak solutions cannot exist globally.

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Sharp upper bound for lifespan of solutions to some critical semilinear parabolic, dispersive and hyperbolic equations via a test function method

Nonlinear Analysis ◽

10.1016/j.na.2018.12.009 ◽

2019 ◽

Vol 182 ◽

pp. 57-74 ◽

Cited By ~ 13

Author(s):

Masahiro Ikeda ◽

Motohiro Sobajima

Keyword(s):

Upper Bound ◽

Function Method ◽

Hyperbolic Equations ◽

Test Function ◽

Semilinear Parabolic ◽

Test Function Method

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Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

10.21203/rs.3.rs-996320/v1 ◽

2021 ◽

Author(s):

Hongcai Ma ◽

Shupan Yue ◽

Yidan Gao ◽

Aiping Deng

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Three Dimensional ◽

Soliton Solutions ◽

Bilinear Method ◽

Test Function ◽

Lump Solutions ◽

Hirota Bilinear ◽

Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

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